What is the LCM and GCF of 72 and 75?

The question "What is the LCM and GCF of 72 and 75?" can be split into two questions: "What is the LCM of 72 and 75?" and "What is the GCF of 72 and 75?"

In the question "What is the LCM and GCF of 72 and 75?", 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 72 and 75 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 72 and 75:

Multiples of 72: 72, 144, 216, 288, 360, 432, etc.

Multiples of 75: 75, 150, 225, 300, 375, 450, etc.

The least multiple on the two lists that they have in common is the LCM of 72 and 75. Therefore, the LCM of 72 and 75 is 1800.

To find the GCF, we first list the factors of 72 and 75 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 72 are all the numbers that can evenly divide into 72, and the factors of 75 are all the numbers that can evenly divide into 75. Here are the factors for 72 and 75:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Factors of 75: 1, 3, 5, 15, 25, and 75.

The greatest factor on the two lists that they have in common is the GCF of 72 and 75. Therefore, the GCF of 72 and 75 is 3.

In summary, the answer to the question "What is the LCM and GCF of 72 and 75?" is 1800 and 3.

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