# Week 1 – Math 10 – Least Common Multiples

This week when I was doing a practice question to find the least common multiples when using numbers’ prime factorizations. I could not figure out why I kept on receiving with the wrong answer, no matter what. What I was doing wrong? I tried doing it over again but came up with the same results. Then after more explanation, I learned that I multiplied the common numbers of the prime factorization twice instead of the once I needed to do. I also now have a useful technique to find the least common multiples.

Firstly, what are the least common multiples? Least common multiples (LCM) are the smallest positive number that can be divisible by both of the numbers. The way to determine the LCM is to take all the prime numbers of one of the numbers and multiply by any additional factors in the other numbers. An easy way to find the common numbers in two prime factorizations for the LCM is to use a Venn diagram. You can take a Venn diagram and put the common numbers from both of the prime factorizations in the middle. After that, put the remaining numbers from their prime factorizations in the other two sides of the Venn diagram. Then multiply all the numbers together for the LCM.

Let’s do exemple: 