Explain how to find the lcm and gcf of a number.

When you find the LCM you are looking for the least common multiple in numbers.
It doesn't matter how many number you have you list the multiples of each number and the number that is the same that comes first is your LCM. For example if you want to find the LCM 21 and 7 the LCM would be 21 because if you list the multiples (count by 20 and 7) 21 is common in both numbers.
When you are looking for the GCF (greatest common factor) you list the factors that go into the number in a list of numbers. The largest number that goes into the set of numbers is your GCF. If there is no number but one, your GCF is 1 for example 3 and 7. one and three both go into 3 and 1 and 7 go into 7 to the common number in both of them are 1. if you have the numbers let say 4 and 8, the number that go into 4 are 1, 2, and 4. The numbers that go into 8 are 1, 2, 4, and 8. As you can see the numbers 1, 2, and 4 are the common but the largest number that is common is 4.
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To find either the Least Common Multiple (LCM) or Greatest Common Factor (GCF) of two numbers, you always start out the same way: you find the prime factorizations of the two numbers. Then you put the factors into a nice neat grid of rows and columns, and compare and contrast and take what you need.

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