Can u always find the LCM for two numbers by multiplying them together? Why or why not

Question

Jaylynn Grant

Mathematics

19 September, 18:41

Can u always find the LCM for two numbers by multiplying them together? Why or why not

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Answers (2)

Know the Answer?

Nayeli · Answer 1

Multiplying two numbers together will not always give you their lowest common multiple. For example, the least common multiple of 2 and 4 is 4. However, most of the time the LCM will be the product of the two numbers.

Derick · Answer 2

When you multiply the two numbers together, you will always find a common multiple, but necessarily the lowest.

Consider 2 and 5. The LCM is 10! Easy enough.

What about 6 and 15? Well, 6 times 15 is 90 ... but the LCM is 30.

The LCM can be found by taking the prime factors of the numbers multiplied together without duplicates.

In that case, 6 = 2*3 and 15 = 3*5. The LCM is 2*3*5 = 30.

Whenever the numbers share a prime factor, just multiplying them together isn't going to give you the LCM because you haven't gotten rid of the duplicates.

(Notice how 90 is 3 times 30)