Question

what is the smallest number that leaves a remainder of 4 when divided by 3, 4, 5, and 6? a. 56

Answer 1

let the required number be ' x '

x = L.C.M ( 3 , 4 ,5 , 6 ) - remainder

x = L.C.M ( 3 , 4 , 5 ,6 ) - 4. _______eq(1)

3 = 3 × 1 , 4 = 2 × 2 , 5 = 5 × 1 , 6 = 3× 2

L.C.M ( 3 , 4 , 5 ,6) = 3 × 2^2 × 5 = 60

now from eq. ( 1) , we get

x = 60 - 4 = 56

therefore,
the required smallest number = 56

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Your Answer : 56
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