What is the LCM and GCF of 12 and 45?

The question "What is the LCM and GCF of 12 and 45?" can be split into two questions: "What is the LCM of 12 and 45?" and "What is the GCF of 12 and 45?"

In the question "What is the LCM and GCF of 12 and 45?", LCM is the abbreviation of Least Common Multiple and GCF is the abbreviation of Greatest Common Factor.

To find the LCM, we first list the multiples of 12 and 45 and then we find the smallest multiple they have in common. To find the multiples of any number, you simply multiply the number by 1, then by 2, then by 3 and so on. Here is the beginning list of multiples of 12 and 45:

Multiples of 12: 12, 24, 36, 48, 60, 72, etc.

Multiples of 45: 45, 90, 135, 180, 225, 270, etc.

The least multiple on the two lists that they have in common is the LCM of 12 and 45. Therefore, the LCM of 12 and 45 is 180.

To find the GCF, we first list the factors of 12 and 45 and then we find the largest factor they have in common. The factors of any number, are all the numbers that you can evenly divide into that number.

In other words, the factors of 12 are all the numbers that can evenly divide into 12, and the factors of 45 are all the numbers that can evenly divide into 45. Here are the factors for 12 and 45:

Factors of 12: 1, 2, 3, 4, 6, and 12.

Factors of 45: 1, 3, 5, 9, 15, and 45.

The greatest factor on the two lists that they have in common is the GCF of 12 and 45. Therefore, the GCF of 12 and 45 is 3.

In summary, the answer to the question "What is the LCM and GCF of 12 and 45?" is 180 and 3.

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