Question

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

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.

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)