# Find three pairs of Numbers for which the least common multiple equals the product of the two numbers?

Question:It said this in my sisters math book. Any answers??

This will be the case for any two numbers that don't have a common factor other than 1.

The easiest groups of two numbers to find would be two prime numbers, whose factors are the number itself and 1.

3 is prime and 7 is prime, so the least common multiple would be 21.

Other groups would include, for example, one even number and one odd number, to reduce the chance of a common multiple. You'll still have to check by writing out the factors of the numbers to see if there is a common factor. If there is, that pair is not an answer.

So, for example, the factors of 8 are 2 and 4. The factor (only one) of 9 is 3. (I'm omitting the number and 1 from the list of factors.) So the LCM of 8 and 9 is 72.

No two even numbers meet the test, because all even numbers have at least one common factor, 2. So the LCM of two even numbers is at least as small as half the product of the numbers, and maybe smaller.
2 and 3
4 and 5
6 and 7

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