### Video Transcript

Find the two numbers whose LCM is 45 and sum is 54.

The least common multiple, or LCM, is the smallest positive number that is a multiple of two or more numbers. In this question, we’re looking for two numbers with an LCM of 45. For two numbers to have an LCM of 45, they must both be factors of 45. The three factor pairs of 45 are one and 45, three and 15, and five and nine as these pairs of numbers multiply to give us 45. In ascending order, the factors of 45 are one, three, five, nine, 15, and 45.

We are also told in the question that the sum of our numbers is 54. Therefore, the two numbers need to add to give us 54. The only two numbers from our list that add to 54 are 45 and nine. We can check that they also have an LCM of 45 by looking at the nine and 45 times table. The smallest number that appears in both of the lines is 45.

The two numbers whose LCM is 45 and sum is 54 are nine and 45.