Question

Find a number such that when it is added to 7249 will be perfectly divisible by 12,14,21,33 and 54

Answer 1

The least number which is divisible by the given numbers is called the Least Common Multiple.

So we shall find the LCM of 12, 14, 21, 33 & 54

The given numbers are 12, 14, 21, 33 & 54

Now

12 = 2 × 2 ×3

14 = 2 × 7

21 = 3 × 7

33 = 3 × 11

54 = 3 × 3 ×3 × 2

The Least Common Multiple is 2 × 3 × 7 × 2 × 9 ×11 = 8316

So 8316 is the least number which is divisible by 12, 14, 21, 33 & 54.

Now 8316 – 7249 = 1067

Hence 1067 must be added to 7249 to make it divisible by 12, 14, 21, 33 & 54