Find the least multiple of 13, which, on dividing by 4, 5, 6, 7 and 8, leaves a remainder 2 in each case.

Correct option is B

Given:

Required number leaves remainder 2 when divided by 4, 5, 6, 7, and 8

The number must be a multiple of 13

Solution:

Let the number be N

If a number leaves remainder 2 when divided by several numbers, then:

N−2 is divisible by 4, 5, 6, 7, 8

N - 2 = LCM(4, 5, 6, 7, 8)

Since, LCM = 840

N = 840k + 2,
Try smallest k such that 840k + 2 is divisible by 13:

Check for k = 1 to ... until divisible by 13:

840(1) + 2 =$$842 \div 13 = 64.77$$​

840(2) + 2 =$$1682 \div 13 = 129.38$$​

840(3) + 2 =$$2522 \div 13 = 194$$​

Least multiple of 13 of the required form is 2522.

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