What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder

September 22, 2023

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Q. What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder of 7 in each case?

(A) 3047

(B) 6047

(C) 7987

(D) 63847

Ans: 7987

Sol:

Number is divided either by 20 or by 42 or by 76

= K × LCM (20, 42, 76) + constant difference

= 7980 K + 7 ( where K is natural number)

So, if we put K = 1 then,

Least number will be 7980 + 7 = 7987

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