Question

Find the least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3.

Answer 1

Given: 2497; divisors = 5, 6, 4 and 3.

Step-wise calculation:

1. Find LCM of 3, 4, 5 and 6.

Prime factors: 3, 4 = 2², 5, 6 = 2 × 3. 

So, LCM = 2² × 3 × 5 = 60.

2. Divide 2497 by 60:

60 × 41 = 2460

Remainder = 2497 – 2460

= 37

3. Least number to add = 60 – 37

= 23

The least number to be added is 23 (2497 + 23 = 2520, which is divisible by 5, 6, 4 and 3).