Question

Find smallest number which when divided by 24, 36 and 54 gives remainder 5 in each case.

Answer 1

Find the smallest number that is divisible by all 3 of your numbers, then add 5 to it. So, first break the numbers into their prime factors: 

24 = 2 * 2 * 2 * 3 

36 = 2 * 2 * 3 * 3 

54 = 2 * 3 * 3 * 3 

So, the smallest number divisible by all 3 is 2 * 2 * 2 * 3 * 3 * 3 = 216. Add 5 to that to get 221.