Find the least number which when divided by 12, 15, 18 and 27 leaves remainders 10, 13, 16 and 25 respectively.

In each case the remainder is 2 less than the divisor (12 − 10 = 15 − 13 = 18 − 16 = 27 − 25 = 2). So the number is 2 less than a common multiple. LCM(12, 15, 18, 27) = 540, so the least number = 540 − 2 = 538.