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:
(Mon, Dec 13, 2010 02:01:49 PM)
Why subtracted 9999-399?
Vishnu said:
(Fri, Jan 28, 2011 01:46:33 AM)
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:
(Fri, Jan 28, 2011 03:00:50 AM)
@vishnu.
How 9000, 9400 and 9800 are not divsible by 40?.
It is divisible by 40.
Gwene said:
(Sun, Jan 30, 2011 07:32:24 AM)
Why only 9999? among those 4 numbers 9800 is greater so why not 9800?
Gwene said:
(Sun, Jan 30, 2011 07:35:37 AM)
Vishnu why should we divide by 40?
Mehar said:
(Mon, Jan 31, 2011 02:16:49 AM)
hai vishnu...why should divide with only 40 why cant we do that with reaming no given there?
Jyoti said:
(Mon, Jan 31, 2011 03:03:38 AM)
@vishnu.
Their is no need to divide by 40.
Debashree said:
(Mon, Feb 14, 2011 09:21:16 PM)
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
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:
(Sun, May 29, 2011 01:39:37 PM)
Good answer rahul.
Neha said:
(Thu, Jun 30, 2011 03:10:20 AM)
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:
(Thu, Jun 30, 2011 04:21:55 AM)
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:
(Sun, Jul 10, 2011 02:46:11 PM)
Find LCM AND HCF OF
x3+2x2-4x-8 and2x3+7x2+4x-4
Arunav said:
(Tue, Jul 26, 2011 03:18:32 PM)
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:
(Fri, Dec 30, 2011 04:41:21 PM)
Friends will you please explain how the LCM came 600 in detail ?
Lakhan said:
(Fri, Dec 30, 2011 04:45:28 PM)
@Rahul
How can you ignore 75= 15 x 5 = 5 x 5 x 3 while calculating LCM ?
Sam said:
(Tue, Jan 3, 2012 04:05:32 PM)
Great explanation Debashree.
Pk Rojer said:
(Mon, Jan 9, 2012 03:00:56 PM)
Instead of calculating LCM Why we don't go for calculating HCF.
Dr.Deepshikha Saini said:
(Fri, Mar 16, 2012 08:11:28 PM)
Debashree you are superb. Thanks for such a wonderful explanation.
Akshata said:
(Sat, Apr 14, 2012 03:25:32 PM)
@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:
(Tue, Apr 17, 2012 08:51:29 PM)
Please calculate the remainder.
Alwin said:
(Wed, May 9, 2012 08:32:10 AM)
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:
(Wed, Aug 29, 2012 04:50:35 PM)
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:
(Sun, Nov 25, 2012 10:48:21 PM)
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:
(Sun, Dec 2, 2012 03:11:03 PM)
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.
Required number (9999 - 399) = 9600.