Question

Find the smallest number which when divided by 18,12,24 leaves a remainder of 16,10 and 22 respectively

Answer 1

If n is any integer that leaves a remainder 16, 10, 22 when divided by 18, 12, 24 respectively, then n+2 is a common multiple of 18, 12, 24. This is the same as saying n+2 is a multiple of lcm(12,18,24)=72
The least positive integer with this property is n=70.