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

Question

Dylan Williams

Mathematics

18 September, 19:54

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

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Answers (1)

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Fatima Garner · 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).