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)
