What is the LCM and GCF of 12 and 35?

The question "What is the LCM and GCF of 12 and 35?" can be split into two questions: "What is the LCM of 12 and 35?" and "What is the GCF of 12 and 35?"

In the question "What is the LCM and GCF of 12 and 35?", 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 35 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 35:

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

Multiples of 35: 35, 70, 105, 140, 175, 210, etc.

The least multiple on the two lists that they have in common is the LCM of 12 and 35. Therefore, the LCM of 12 and 35 is 420.

To find the GCF, we first list the factors of 12 and 35 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 35 are all the numbers that can evenly divide into 35. Here are the factors for 12 and 35:

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

Factors of 35: 1, 5, 7, and 35.

The greatest factor on the two lists that they have in common is the GCF of 12 and 35. Therefore, the GCF of 12 and 35 is 1.

In summary, the answer to the question "What is the LCM and GCF of 12 and 35?" is 420 and 1.

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