Question

Find the least counting number which when divided by five give a remainder of one and divided by 12 gives a remainder of three

Answer 1

51

Explanation:

We can consider up to 5 multiples of 12:

(0·12 +3) ÷ 5 = 0 r 3

(1·12 +3) ÷ 5 = 3 r 0

(2·12 +3) ÷ 5 = 5 r 2

(3·12 +3) ÷ 5 = 7 r 4

(4·12 +3) ÷ 5 = 10 r 1

The number we're looking for is 51.