Question

What is the least multiple of 7, which when divided by 2, 3, 4, 5 and 6 leaves the remainders 1, 2, 3, 4 and 5 respectively?

Answer 1

35 if divided by 2,3,4,5,6 leaves remainder 1,2,3,4,5

Answer 2

TO FIND :

Least multiple of 7, which when divided by 2, 3, 4, 5 and 6 leaves the remainders 1, 2, 3, 4 and 5 .

SOLUTION :

◆Avoid all even multiples of 7,

such as 14,28,56 etc.. because all these are exactly divisible by 2 , this can't leave a remainder 1.

◆LCM of 2, 3, 4, 5, 6 is 60.The difference in remainders with the divisors is 1.

So , LCM of divisors - 1 = 59.

◆The number will be

constant × LCM of divisors + 59

◆N=60x + 59.

◆x =0 , N =59 . Not a multiple of 7

◆x =1 , N =119 . Multiple of 7.

◆Thus, 117 is the answer.

ANSWER :

Least multiple of 7, which when divided by 2, 3, 4, 5 and 6 leaves the remainders 1, 2, 3, 4 and 5 is 119.