Aptitude - Problems on H.C.F and L.C.M - Discussion

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.5)

5. 

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

[A]. 9000
[B]. 9400
[C]. 9600
[D]. 9800

Answer: Option C

Explanation:

Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399.

Required number (9999 - 399) = 9600.


Ram said: (Jul 14, 2010)  
How to find the l.c.m number the value is 600?

Thom said: (Aug 14, 2010)  
How to find 600 is LCM?

Nitya said: (Sep 14, 2010)  
Just find the lcm of 15, 40, 25, 75.

Then you will get the answer as 600.

Darshana said: (Oct 27, 2010)  
How to find the l.c.m number the value is 600?

Rahul said: (Oct 28, 2010)  
To find the LCM use prime factorization:
15: 5 x 3
25: 5 x 5
40: 5 x 8 = 5 x 2 x 2 x 2
75: 15 x 5 = 5 x 5 x 3
LCM: Every prime factor such that none are repeated:
5 x 3 (from 15) x 5 (from 25) x 2 x 2 x 2 (from 40) and since two 5s and 3 are already there you dont take anything from 75.
so LCM is 5 x 3 x 5 x 2 x 2 x 2 = 600

Then just find the greatest 4 digit number divisible by 600. Which is shown and explained well by the problem explanation.

Pavan said: (Dec 13, 2010)  
Why subtracted 9999-399?

Vishnu said: (Jan 28, 2011)  
Just check if the answers are divisible by 40(one of the numbers given)...It's easy to notice that 9000,9400 and 9800 will not be divisible. So, it's obviously 9600.

Aparna said: (Jan 28, 2011)  
@vishnu.

How 9000, 9400 and 9800 are not divsible by 40?.

It is divisible by 40.

Gwene said: (Jan 30, 2011)  
Why only 9999? among those 4 numbers 9800 is greater so why not 9800?

Gwene said: (Jan 30, 2011)  
Vishnu why should we divide by 40?

Mehar said: (Jan 31, 2011)  
hai vishnu...why should divide with only 40 why cant we do that with reaming no given there?

Jyoti said: (Jan 31, 2011)  
@vishnu.

Their is no need to divide by 40.

Debashree said: (Feb 14, 2011)  
Wow should we divide 9999 by 600

i) 1st we find the greatest 4 digit number

ii) Then find the lcm of 15,25,40 ,75 ,is 600 ,so 600 is least number by which 15,25,40,75.so all the multiple of 600 is divisible by 15,25,40,75

iii) Then find multiple of 600 which is less than 999

iv) So we divide 9999 by 600

and get 399 as remainder,

If substract 399 from 9999 tnen we get that number

9999 - 3999 = 9600

Vaani said: (Apr 28, 2011)  
Why to subtract remainder from 9999 ?

Sravanreddypailla said: (Apr 28, 2011)  
We have to find greatest 4 digit number so it may be between 9000 to 9999 let the number be x

this x should be divisible by 15, 25, 40 and 75 so take common least nnumber from all factors i.e l.c.m=600

therefore x is also divisible by 600 that means when x is divided by 600 remainder should be '0' but how can we find that number??

that number x lies between 9000 to 9999

take any number between them i.e take 9000,..9010,...9090...9900...9997,9998,9999 as your wish

so insted of 9999 here iam taking 9998 which is divided by 600

so remainder is 398 so substract 398 from 9998 i.e 9998-398=9600

why we wre substracting is because x should be divisible 600 and
remaider should be '0' so x is 9600 thats it

Bhargav said: (May 29, 2011)  
Good answer rahul.

Neha said: (Jun 30, 2011)  
Find the LCM of 15, 25, 40 and 75 which is 600.

Now, find out the multiples of 600 i.e.
600*1=600
600*2=1200
600*3=1800
........
600*16=9600
600*17=10200

We can see that the greatest number of four digits is 9600 and hence 9600 is the answer.

Rachna said: (Jun 30, 2011)  
Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.
(I understood till above, but how come 9999 divided by 600 is 399??)

On dividing 9999 by 600, the remainder is 399??

Required number (9999 - 399) = 9600??

Sameer said: (Jul 10, 2011)  
Find LCM AND HCF OF
x3+2x2-4x-8 and2x3+7x2+4x-4

Arunav said: (Jul 26, 2011)  
There can be another approach. Just find the L.C.M. of the nos. The L.C.M. comes to be 600. Now check which is the greatest no. which is getting divided by 600.

Numbers of option B and option D are not getting divided by 600 and between option B and C (which are getting divided by 600) the number of option C is the greatest no. divisible by 600

In this way I guess it would be quicker than dividing 9999 and then subtracting the remainder.

Lakhan said: (Dec 30, 2011)  
Friends will you please explain how the LCM came 600 in detail ?

Lakhan said: (Dec 30, 2011)  
@Rahul

How can you ignore 75= 15 x 5 = 5 x 5 x 3 while calculating LCM ?

Sam said: (Jan 3, 2012)  
Great explanation Debashree.

Pk Rojer said: (Jan 9, 2012)  
Instead of calculating LCM Why we don't go for calculating HCF.

Dr.Deepshikha Saini said: (Mar 16, 2012)  
Debashree you are superb. Thanks for such a wonderful explanation.

Akshata said: (Apr 14, 2012)  
@Arunav.

Your explanation seems to be quick and fast. Can you elaborate and let me know who will it work.

My funds of finding LCM in this case 600 is clear.

But when you are writing "Numbers of option B and option D are not getting divided by 600 and between option B and C (which are getting divided by 600) the number of option C is the greatest no. Divisible by 600" is not clear. Just let me know the explanation.

In this way I guess it would be quicker than dividing 9999 and then subtracting the remainder.

Aslam said: (Apr 17, 2012)  
Please calculate the remainder.

Alwin said: (May 9, 2012)  
To find LCM
15=3*5
25=5*5
40=2*2*2*5
75=3*5*5
Every number written in the form of multiples of prime number
Now we will write as
15=> 3 5
25=> - 5 5
40=> - 5 - 2 2 2
75=> 3 5 5 - - -
___________________
3 5 5 2 2 2
Then
3*5*5*2*2*2=600

Hence the result

Dileep Kumar M B said: (Aug 29, 2012)  
How a person could know whether to take LCM or HCF? can anybody explain me when should we use these LCM and HCF ?

Rahul Vasu said: (Nov 25, 2012)  
Calculating without LCM method

Shortcut way to get 600

In the option A) is given 9000 and B) 9400 and C) 9600 and D) 9800

To subtract from highest number first i.e (D-C) 9800-9600= 200 and (B-A) 9400-9000= 400

Now (D-C)=200
(B-A)=400

Add 200 + 400= 600

The questions says greatest four digit that means in every first digit is 9..so therefore there will be 4 greatest digits of 9 i.e is 9999

Hence 9999-600= 9,399
(Therefore the first digit is 9 so the rest 3 digit is 399 and hence 9999 - 399)

9999-399= 9600

Ravi said: (Dec 2, 2012)  
We need to find highest 4 digit least common multiplier. So lcm of given numbers is 600. It's a three digit number but need to find 4 digit number. 600*8=4800 but I still need to be in range below 10000. 4800*2=9600.

Ram said: (Jun 10, 2013)  
How to find 600 is LCM?

Priya said: (Jul 28, 2013)  
LCM of 15: 5 X 3.

25: 5^2.

40: 5 X 2^3.

75: 5^2 X 3.

From each highest power of 5 = 5^2, 2 = 2^3, 3 = 3.

So 5^2 X 2^3 X 3 = 600.

Vinod said: (Aug 27, 2013)  
I don't know how to do LCM & HCF, anyone can you help me how to do?

S. Nganba Ypk said: (Aug 31, 2013)  
L.C.M. of 15, 25, 40 and 75 is 600.

Now, We find out the multiples of 600 of lowest/smallest five digit number i.e.600*17=10200.

Therefore, Greatest four digit number divisible by 15, 25, 40 and 75 can easily found by 600*16 i.e 9600.

This is simplest & easiest method.

Ankit said: (Sep 13, 2013)  
When greatest FOUR Digit number is to be found it means the number wont exceed 9999 so when we take 600 modulus 9999 we get remainder 399 which means that we are having 399 left after dividing 9999 with 6000 so we subtract 399 from 9999 so that remainder becomes zero and we get the greatest 4 digit number.

As the LCM of four number is 600 the number divisible by them are multiple of 600 i.e.

600
1200
1800
2400
3000
3600
4200
4800
5400
6000
6600
7200
7800
8400
9000
9600 <----- this is the greatest 4 digit no. divisible
10200

Ann said: (Oct 6, 2013)  
How do we know whether to find lcm or hcf?

Soumya said: (Dec 14, 2013)  
Why do we use LCM instead of HCM?

Sruthi said: (Jan 4, 2014)  
5) 15,25,40,75
------------
5) 3,5,8,15
------------
3) 3,1,8,3
------------
1,1,8,1

Now,

LCM = 5*5*3*8 = 600.

Achutha said: (Jan 19, 2014)  
Please tell why we have to take lcm instead instead of hcf and in which situation I have to take lcm or hcf?

Tejas Kumbhar said: (Feb 8, 2014)  
The Logic here is this:

We have to find the greatest 4 digit number which is divisible by 15, 25, 40 and 75, hence it is a multiple of all these.

The LCM(15, 25, 40, 75) = 600 i.e. the least common multiple.

Hence all other common multiples of 15, 25, 40 and 75 will be multiples of 600 as well.

So to find the highest 4 digit one among all the common multiples, divide all the options by 600 to check which is perfectly divisible by 600. We get 9600, which is the answer.

Shubhangi said: (Apr 14, 2014)  
Why do we take LCM of the given numbers, but not HCF?

Sanesh said: (Jul 23, 2014)  
How you get 399?

Heena said: (Aug 3, 2014)  
We can also take 9800 as a base then we have to divide 9800 by 600 which gives 200 remainder and we subtract 200 from 9800 will give the answer 9600.

Atul said: (Sep 27, 2014)  
How to devide 9999 by 600? please explain.

Rohir said: (Oct 1, 2014)  
How that remainder come 399 please tell me?

Veeramani said: (Oct 5, 2014)  
9999 divide 600 which give only remainder for 133 but there they are said 399 how its?

Anil said: (Oct 31, 2014)  
What if we take 6 digits?

Siddharth said: (Nov 19, 2014)  
Hi all,

Another method to answer this question is just break all four (15, 25, 40, 75) in to prime numbers.

15 = 5*3.
25 = 5*5.
40 = 8 (2*2*2) *5.
75 = 5*3*5.

Now here we can see the common divisors are 5, 3 and 8.

So the number which is divisible by 5, 3 and 8 is the right answer which is option C 9600.

Sagar said: (Feb 21, 2015)  
How remainder 399 comes, by my calculation remainder must be 133? Please show the remainder calculation.

Manish said: (Mar 14, 2015)  
Why we have taken LCM of following numbers when the question is about the greatest number which suggests HCF?

Shabnam said: (Mar 18, 2015)  
Where is the come 399? I am totally confuse some one define me.

Satish Kumar said: (Mar 20, 2015)  
Guys don't worry. You can do this by another method.

From options 9800 is highest number so divide it with given numbers 15, 25, 40, and 75. But 75 is not divisible so forget about 9800.

Now choose the next highest number from given options that is 9600. And it is divisible by all the given numbers. That is the answer.

Don't worry about remaining options because according to the question we need the highest number.

Konika said: (Apr 7, 2015)  
How we get greatest number of 4 digit 9999?

Yugam Wadhwa said: (May 3, 2015)  
After finding 600 we have to find the maximum 4 digit multiple of 600, because it will also be divisible by four numbers.

Thus 600 is divided by 9999 and remainder is 399. Remainder is subtracted because if we divide (9999-399=x)x, it will completely divide.

Abdul said: (May 21, 2015)  
How can I divide 9999/600 to get 399? Can you please clearly elaborate it?

Sangeet said: (Jun 19, 2015)  
Hi, I do not when to use HCF & when to use LCM?

Here it is mentioned the word "GREATEST" but still we find LCM instead of HCF why?

Daisy Chowdhury said: (Jul 1, 2015)  
I use the same technique and I am agree with the first one. Now I am much confident about with dealing the sum.

Mahesh said: (Jul 9, 2015)  
25 /__15,25,40'75___
3 /__15,1,40,3____
5 /__5,1,40,1____
1,8,1

If we do LCM by following above procedure we are getting the LCM as.

25*3*5*8 = 3000.

So may I know why we are getting the wrong one?

Nandha said: (Jul 13, 2015)  
Why we have to subtract (9999-399)?

Gayathri Ganesan said: (Jul 26, 2015)  
Magesh, I'm also getting confusion with that type of doing lcm brings 3000. Then how they put 600? Is anyone cleared this doubt?

David said: (Aug 7, 2015)  
Because greatest no. of four digit is only 9999.

So we divide 9999 by 600. So please use your common sense.

V!Cky said: (Sep 5, 2015)  
9800-9000 = 800.

9600-9400 = 200.

800-200 = 600.

Solved further get 399.

Prajnya.Samantaray said: (Sep 20, 2015)  
Can any one please explain in which case I have to take the L.C.M and where H.C.F? I am really confused.

Amala said: (Oct 30, 2015)  
Any body please tell me how we get 399 remainder?

Gayathri said: (Dec 5, 2015)  
Is anybody got idea about different lcm value by two methods?

Darshan said: (Dec 24, 2015)  
Concept is simple.

The greatest 4 digit no in numbers is 9999.

Then find the LCM of 15, 25, 40, 75 = that is 600.

So if 9999 is divisible by 600 then it is the greatest 4 digit no.

If we divide 9999 by 600 it will leave a remainder 399.

600) 9999 (16
9600
--------
0399 --< this is remainder.

If we subtract it with dividend :: (9999-399) = 9600.

So the 9600 is divisible by 600 without leaving a remainder hence it is divisible by all given nos.

Kinjal said: (Feb 18, 2016)  
9999 is divided by 600.

Quotient: 16.

Remainder: 399.

Vivek Balodi said: (Mar 15, 2016)  
Why we take LCM of these Numbers ? Why Not HCF? Can Anyone explain ? When we have to take LCM and when HCF?

Sri said: (Apr 27, 2016)  
Why are you not divide 600 by 96000, which is exactly divisible?

Please tell me.

Pravin said: (May 27, 2016)  
5) 15,25,40,75
------------
5) 3,5,8,15
------------
3) 3,1,8,3
------------
1,1,8,1

Now,
LCM = 5 * 5 * 3 * 8 = 600

LCM = 600.

600)9999(16
-------------
600
3999
3600
399 --> reminder.

9999 - 399 = 9600 answer.

Atul said: (Jun 1, 2016)  
@Pravin.

I agree with you. Thank you.

Kanwar Jackson said: (Jun 9, 2016)  
399 is subtracted so that the number may be exactly divided.

To understand this, take an example.

If we divide 20 by 3, the remainder is 2. So 20 is not divisible by 3 but if I subtract remainder from it i.e. 20 - 2 = 18, now it will be exactly divisible by 3. (ie) 18/3 = 6.

Hope this helps!

Prakasg said: (Jul 9, 2016)  
Nice explanation.

Mahima said: (Jul 24, 2016)  
Find the greatest 3-digit number which is exactly divisible by 4,8 and 12?

Anyone solve this?

Tina said: (Jul 25, 2016)  
Please explain me if the 2 are already repeated in 25 then why you have taken for 3 times?

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