Question

Find the least number which when divided by 12, 27 and 35 leaves 6 as a reminder?

Answer 1

Find the least number which when divided by 12, 27 and 35 leaves 6 as a remainder?

Answer :- 3774. 3780.

Answer 2

Given: Three numbers 12, 27 and 35

To find: The least number which when divided by given numbers, leaves remainder 6

Solution: To find the required number, first we need to find the least number which is exactly divisible by 12, 27 and 35 which is their LCM.

Using prime factorization method:

12 = 2 × 2 × 3

27 = 3 × 3 × 3

35 = 5 × 7

LCM is the product of maximum frequencies of all the factors of given numbers.

LCM = 2 × 2 × 3 × 3 × 3 × 5 × 7 = 3780

So, 3780 is the least number which is exactly divisible by the given numbers.

Th required number will be 3780 + 6 i.e., 3786.

Hence, the least number which when divided by 12, 27 and 35 leaves remainder 6 is 3786.