Find the least positive integer which on diminished by 5 is exactly divisible by 36 and 54.

In this type of problem we need to calculate L.C.M. of these two numbers so first we calculate the L.C.M.

Factor of 36 is = 2 × 2 × 3 × 3

Similarly factor of 54 is = 2 × 3 × 3 ×3

So L.C.M. of 36 and 54 is = 2 × 2 × 3 × 3 × 3

= 108

So the least positive integer is = 108 + 5

= 113

Hence 113 is the lest positive integer which on diminished by 5 is exactly divisible by 36 and 54.