Question 53

A natural number, when divided by 4, 5, 6 or 7, leaves a remainder of 3 in each case.
Whatis the smallest of all such numbers?

Solution

To find the LCM of 4, 5, 6 or 7,

5 = 5

4 = 2 x 2

6 = 2 x 3

7 = 7

LCM = 5x 2 x 2 x 3x7 = 420

leaves remainder 3 in each case we take 420 + 3 = 423

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A natural number, when divided by 4, 5, 6 or 7, leaves a remainder of 3 in each case.Whatis the smallest of all such numbers?