This week in math 10, I learned how to find the lowest common multiple (LCM) of two numbers. Below are the steps to finding an LCM.
Step 1: Find the prime factors of two numbers (ex. 12 and 54).
Personally, I like to use factor trees, but if the numbers are smaller, or if I know the factors of the number off the top of my head I usually won’t. When I do make factor trees, I also like to circle the prime factors, as it makes it easier for me to identify them when I need to use them later on in the problem.
Step 2: Organizing prime factors
Once you have the prime factors of both numbers, it helps to organize them based on value, eg. smallest to largest. It also helps to write these numbers as if you were going to multiply them as is; even though you don’t multiply them now, that will happen later.
Step 3: Finding common factors
This step is pretty self – explanatory: find the common prime factors within the two numbers.
Step 4: Combining prime factors
Here, the numbers are reorganized like this: if there is one common number, add that number to the list the number of times it appears, for example 2 appears once, so you write down 2, and 3 appears once so you write down 3. If there were two 2’s in both of the numbers, then you would write 2 times 2 instead of just having one.
Then, multiply the the common prime factors by the rest of them.
Step 4.5
Reorganize the numbers, from least to greatest.
Step 5: Exponents
Write the equation using exponents (ex. if there are two 2’s, 2 to the power of 2)
Step 6: Solve the exponents
Step 6.5: Multiply the numbers
Below is the whole equation:
