What is the smallest number when added by 5 the summation will be divided by 12, 16, 24 and 32?

Question: What is the smallest number when added by 5 the summation will be divided by 12, 16, 24 and 32?

Solution:
The required number will be 5 less than L.C.M. of 12, 16, 24 and 32.

12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
32 = 2 × 2 × 2 × 2 × 2

So the L.C.M of 12, 16, 24 and 32 = 96

Required number= 96 - 5 = 91