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LCM: (Least Common Multiple)
The two most common methods of finding the LCM of two numbers are the Listing method and the Prime Factorization method.
The Listing Method: List the multiples of the larger number until you find a common product that is divisible by the smaller number.
Example: To find the least common multiple of 6 and 8:
The Prime Factorization Method: This method is most useful if the numbers that you are trying to determine their LCM is very large.
Example: Find the LCM of 36 and 90:
Step 1: Find the prime factorization of both numbers:
Step 2: List all the base numbers of the factors. As you see from above, you have a 2, 3, and a 5. Take the largest exponential value of all these numbers and multiply them.
Look you have 22 and 2 – take the 22. (only once)
Next you have 32 – take the 32 (only once)
Next you have a 5 – take the 5
Multiply all the values that you have taken:
2 2· 32 · 5 =
4 · 9 · 5 =
45 · 5 = 180 so the LCM is 180