Exercise 39 Page 37

Now, we can write the factor pairs of each number by finding the product of two factors that equals 84.

Remember that when a number is multiplied by an integer, the result is a multiple of the first number.

Notice that these products have the same form as the products we used to find the factor pairs. Then, we can list these products to identify the numbers that have 84 as a multiple. Let's do it! 1 * 84 &= 84 → 84 is a multiple of 1 84 * 1 &= 84 → 84 is a multiple of 84 2 * 42 &= 84 → 84 is a multiple of 2 42 * 2 &= 84 → 84 is a multiple of 42 3 * 28 &= 84 → 84 is a multiple of 3 28 * 3 &= 84 → 84 is a multiple of 28 4 * 21 &= 84 → 84 is a multiple of 4 21 * 4 &= 84 → 84 is a multiple of 21 6 * 14 &= 84 → 84 is a multiple of 6 14 * 6 &= 84 → 84 is a multiple of 14 7 * 12 &= 84 → 84 is a multiple of 7 12 * 7 &= 84 → 84 is a multiple of 12 Now, we can list the multiples of the numbers that are factors of 84 to find a pair of numbers with a least common multiple equal to 84. Let's ignore the 1 and 84 because they are the identities. Multiples of2&: 2,4,6,8,10,12,14,16,18,20,... Multiples of3&: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,... Multiples of4&: 4,8,12,16,20,24,28,32,36,... Multiples of6&: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54,.. Multiples of7&: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 ,... Multiples of42&: 42, 84, 126, 168, 210, 252, 294, ... Multiples of28&: 56, 84, 112, 140, 168, 196, 224, 252,... Multiples of21&: 21, 42, 63, 84, 105, 126, 147, 168, ... Multiples of14&: 14, 28, 42, 56, 70, 84, 98, 112, 126,.. Multiples of12&: 12, 24, 36, 48, 60, 72, 84, 96, 108,... From the above list, we can see that 42, and 28 have a LCM of 84. There are other pairs of numbers with an LCM of 84. This is just one example pair.