What is the LCM and GCF of 36 and 90?

The question "What is the LCM and GCF of 36 and 90?" can be split into two questions: "What is the LCM of 36 and 90?" and "What is the GCF of 36 and 90?"

In the question "What is the LCM and GCF of 36 and 90?", 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 36 and 90 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 36 and 90:

Multiples of 36: 36, 72, 108, 144, 180, 216, etc.

Multiples of 90: 90, 180, 270, 360, 450, 540, etc.

The least multiple on the two lists that they have in common is the LCM of 36 and 90. Therefore, the LCM of 36 and 90 is 180.

To find the GCF, we first list the factors of 36 and 90 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 36 are all the numbers that can evenly divide into 36, and the factors of 90 are all the numbers that can evenly divide into 90. Here are the factors for 36 and 90:

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

The greatest factor on the two lists that they have in common is the GCF of 36 and 90. Therefore, the GCF of 36 and 90 is 18.

In summary, the answer to the question "What is the LCM and GCF of 36 and 90?" is 180 and 18.

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