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

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.

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)