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. 12)
12.
The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
Answer: Option
Explanation:
L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
Number to be added = (60 - 37) = 23.
Discussion:
40 comments Page 1 of 4.
Varshini said:
2 years ago
The remainder becomes 37.
(2)
Aideu Sondikoi said:
3 years ago
Simple, if a number is divisible by 4 numbers, then the number will also divisible by their least common multiple. say, 50 is divided by 2,5,10,25.
Then lcm of (2, 5,10,25) is 50. So, 50 is divisible by 50.
So in the question, the number will divisible by lcm of the numbers, 60.
60k= 2497 + n.
We have to add a number for 60 to completely divide 2497.
Check options its 23.
2497 + 23 = 2520/60.
Then lcm of (2, 5,10,25) is 50. So, 50 is divisible by 50.
So in the question, the number will divisible by lcm of the numbers, 60.
60k= 2497 + n.
We have to add a number for 60 to completely divide 2497.
Check options its 23.
2497 + 23 = 2520/60.
(5)
Kanishka Roy said:
5 years ago
@Tanya.
60 is the LCM of 5,6,4,3.
The keyword being Least in LCM. So any multiples of 60 should also be a multiple of 5,6,4,3.
So we divide 2497 by 60. Now we get 37 as remainder and quotient as 41. The question is how much should we ADD, so we find the next product which is 42.
Hence, (60*42) - 2497=23. This is the answer.
Hope you understood!
60 is the LCM of 5,6,4,3.
The keyword being Least in LCM. So any multiples of 60 should also be a multiple of 5,6,4,3.
So we divide 2497 by 60. Now we get 37 as remainder and quotient as 41. The question is how much should we ADD, so we find the next product which is 42.
Hence, (60*42) - 2497=23. This is the answer.
Hope you understood!
(13)
Tanya said:
5 years ago
Why we divide 2497 by 60? Please explain.
(2)
Sathri Prashanthi said:
5 years ago
Why 60-37? Explain.
(5)
Rinkal said:
5 years ago
How we get the remainder 37?
(1)
Ranjith said:
7 years ago
Great answer, Thanks @Anita.
(2)
Lizzy said:
7 years ago
Dividing 2497 by the lcm of 5, 6, 4, 3 (which is 60, btw) gives 37 as remainder. (41 is the quotient)
Subtracting 37 from 2497 we get 2460 which is the nearest number divisible by 60.(2520 is the next number)
2460+60=2520.
Break the equation (2460+37)+23=2520
2497 + 23= 2520.
23 is the least number that should be added to 2497 so that the sum is divisible by 60!.
Subtracting 37 from 2497 we get 2460 which is the nearest number divisible by 60.(2520 is the next number)
2460+60=2520.
Break the equation (2460+37)+23=2520
2497 + 23= 2520.
23 is the least number that should be added to 2497 so that the sum is divisible by 60!.
(5)
Saumya singh said:
7 years ago
On dividing 2497 by 60 so the remainder will not become 37. The right remainder will become 41.61.
So why it is 37 here, could you please explain?
So why it is 37 here, could you please explain?
(4)
Nav said:
7 years ago
60*41=2460+60=2520-2497 = 23.
(2)
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