Common multiples

A number is a common multiple of 4 and 6. It is between 50 and 70. What is the number? Try it first. Pause if you like. A multiple is a number we reach by counting on in equal steps. Here, we need the lists for 4 and for 6. We only need numbers between 50 and 70. 4 times 13 equals 52. So 52 is a multiple of 4. 4 times 14 equals 56. Add 4 to reach the next multiple. 4 times 15 equals 60. Add 4 to reach the next multiple. 4 times 16 equals 64. Add 4 to reach the next multiple. 4 times 17 equals 68. Add 4 to reach the next multiple. Multiples of 4 between 50 and 70 are 52, 56, 60, 64 and 68. 6 times 9 equals 54. So 54 is a multiple of 6. 6 times 10 equals 60. Add 6 to reach the next multiple. 6 times 11 equals 66. Add 6 to reach the next multiple. Multiples of 6 between 50 and 70 are 54, 60 and 66. Which number appears in both lists? A number on just one list will not do. Line up the values from the two lists. Look for a match. 60 is 15 times 4 and also 10 times 6. So it is a multiple of both numbers. 60 is between 50 and 70. The number is 60. A common multiple is a number on both lists of multiples.

Find the first common multiple of 6 and 8. Try it first. Pause if you like. This time, we want the first number shared by the two lists. Start with the smallest multiples. Count in sixes: 6, 12, 18, 24, and so on. Count in eights: 8, 16, 24, and so on. Which is the first number on both lists? Put the values in line. Look from the smallest upwards. 24 is 4 times 6 and also 3 times 8. The first common multiple of 6 and 8 is 24. A common multiple is on both lists. The first common multiple is the smallest number they share.