Question

Least common multiple of two numbers one of the numbers is seven less than the other number what are the numbers? Justify your answer.

Answer 1

Let x represent the first number, then x-7 represents the second number

Assume the numbers are whole numbers (no negative numbers), then the smallest value that x could be is 8. Thus, the first number is 8 and the second number is 1. The LCM is 8.

Let's increase x by one number so that x=9, then the second number is 2. The LCM is 18.

Let's increase x again by one number so x=10, then the second number is 3. The LCM is 30.

You could continue this to discover that the LCM will be x(x-7) between x=8 and x=13.

So what happens at x=14? First digit is 14 and the second digit is 7. The LCM is 14.

This will occur for all x-values that are multiples of 7.

Answer: when x is a multiple of 7, the LCM is x. when x is not a multiple of 7, the LCM is x(x-7).