Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : 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:
Answer: Option
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.
Discussion:
120 comments Page 3 of 12.
Satti said:
7 years ago
Let consider 15 which is div by 3. Check 9000, 9400, 9600, 9 800 is divisible or not.
We know 9400 and 9800 are not divisible. Hence we omitting that two.
Again look for 9000 and 9600. We have 15, 25, 40, 75 by simply seeing these numbers all are not divided num 9000. Hence our answer is 9600.
We know 9400 and 9800 are not divisible. Hence we omitting that two.
Again look for 9000 and 9600. We have 15, 25, 40, 75 by simply seeing these numbers all are not divided num 9000. Hence our answer is 9600.
Kanwar Jackson said:
9 years ago
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!
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!
Rasika shelke said:
9 years ago
Greatest 4 digit number = 9999.
LCM = 15, 25, 40, 75.
15 = 5 * 3.
20 = 5 * 5.
40 = 5 * 2 * 2 * 2.
75 = 5 * 5 * 3.
Then the lcm is => 5 * 5 * 2 * 2 * 2 * 3 = 600.
So, divide greatest number by 600.
9999/600 = 399.
Required number = (9999 - 399) = 9600.
So option "c".
LCM = 15, 25, 40, 75.
15 = 5 * 3.
20 = 5 * 5.
40 = 5 * 2 * 2 * 2.
75 = 5 * 5 * 3.
Then the lcm is => 5 * 5 * 2 * 2 * 2 * 3 = 600.
So, divide greatest number by 600.
9999/600 = 399.
Required number = (9999 - 399) = 9600.
So option "c".
S. Nganba Ypk said:
1 decade ago
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.
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.
Alwin said:
1 decade ago
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
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
Chahat Mishra said:
5 months ago
Here's the Easy trick:.
The numbers are 15, 25, 40, 75 are multiples of 5.
And check it's divisible by 5.
Now through options:.
A: 9+0+0+0=9 -> not div by 5,
B: 9+4+0+0=13 -> not div by 5,
C: 9+6+0+0=15 ->divisible by 5.
So, option C is the answer.
The numbers are 15, 25, 40, 75 are multiples of 5.
And check it's divisible by 5.
Now through options:.
A: 9+0+0+0=9 -> not div by 5,
B: 9+4+0+0=13 -> not div by 5,
C: 9+6+0+0=15 ->divisible by 5.
So, option C is the answer.
(29)
Yugam Wadhwa said:
1 decade ago
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.
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.
Mahesh said:
1 decade ago
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?
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?
Pravin said:
9 years ago
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.
------------
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.
Rachna said:
1 decade ago
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??
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??
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