Question

FIND the least number which when divided by 12;16;24;and36 leaves a remainder 7 in case

Answer 1

Solution :

In the question, we are asked smallest number which leaves remainder 7.

So, required number will be 7 more than LCM.

∴ Required number = LCM + 7

Now, finding the LCM of 12, 16, 24 & 36 by prime factorization method.

12 = 2 × 2 × 3

16 =2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

∴ LCM = 2 × 2 × 2 × 2 × 3 × 3

          = 16 × 9 = 144

So, required number = LCM + 7

                                   = 144 + 7

                                   = 151

The least number which when divided by 12,16,24 and 36 leaves a remainder 7 in each case is 151.