The least common multiple of 5, 12 and 24 is 120. This multiple can be found by looking at the common prime factors of the three numbers.
Five is a prime number already, so it does not need to be factored. Twelve has three prime factors: 2 x 2 x 3. Twenty-four has four prime factors: 2 x 2 x 2 x 3. The way to find the least common multiple is to take the highest number of occurrences of the same number. That is, in this problem, 12 has two 2s as prime factors while 24 has three 2s. Therefore, when multiplying for the least common multiple, the problem solver will need to use three 2s. Both 12 and 24 only have one 3, so the problem solver needs to use one 3, as well as one 5 from the original prime number. The problem solver then multiplies them together, 2 x 2 x 2 x 3 x 5, to get 120.