Question

Determine the smallest number which leaves remainder 6&10 when divided by 24&28

Answer 1

Let the number be n.

n = 24a + 6 … (1)

n = 28b + 10 … (2)

equating (1) and (2)

24a + 6 = 28b + 10 or

24a - 28b = 10 - 6 = 4 or

6a - 7b = 1, or

6a = 7b + 1 …(3)

The smallest value of a which can satisfy (3) is 6.

6x6 = 7b + 1 or 36 -1 = 35 = 7b or b = 5.

from (1) we get n = 24x6 + 6 = 150 and from (2), n = 28x5 + 10=150.

So the number is 150.