We want to find three numbers that have a least common multiple of 45. Recall that a factor pair is a combination of two factors that can be multiplied together to equal a number. Let's find the factor pairs of 45 by listing their factors!
Factors of45&: 1, 3, 5, 9, 15, 45
Now, we can write the factor pairs of each number by finding the product of two factors that equals 45.
Number
Product of Two Factors
Factor Pairs
45
1 * 45 =45 3 * 15 =45 5 * 9 =45
(1, 45), (3, 15), (5, 9)
Remember that when a number is multiplied by an integer, the result is a multiple of the first number.
Note that the above 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 45 as a multiple. Let's do it!
1 * 45 &= 45 → 45 is a multiple of 1
45 * 1 &= 45 → 45 is a multiple of 45
3 * 15 &= 45 → 45 is a multiple of 3
15 * 3 &= 45 → 45 is a multiple of 15
5 * 9 &= 45 → 45 is a multiple of 5
9 * 5 &= 45 → 45 is a multiple of 9
Now, we can list the multiples of the numbers that have 45 as a factor to find three numbers with a least common multiple equal to 45. Let's ignore the 1 and 45 because they are the identities.
Multiples of3&: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...
Multiples of5&: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,...
Multiples of9&: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90,...
Multiples of15&: 15, 30, 45, 60, 75, 90, 105, 120,...
From the above list, we can see that 5, 9, and 15 have a LCM of 45. This is just an example set of numbers whose LCM is 45. There may be others!
