What is the LCM and GCF of 17 and 14?

The question "What is the LCM and GCF of 17 and 14?" can be split into two questions: "What is the LCM of 17 and 14?" and "What is the GCF of 17 and 14?"

In the question "What is the LCM and GCF of 17 and 14?", 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 17 and 14 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 17 and 14:

Multiples of 17: 17, 34, 51, 68, 85, 102, etc.

Multiples of 14: 14, 28, 42, 56, 70, 84, etc.

The least multiple on the two lists that they have in common is the LCM of 17 and 14. Therefore, the LCM of 17 and 14 is 238.

To find the GCF, we first list the factors of 17 and 14 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 17 are all the numbers that can evenly divide into 17, and the factors of 14 are all the numbers that can evenly divide into 14. Here are the factors for 17 and 14:

Factors of 17: 1 and 17.

Factors of 14: 1, 2, 7, and 14.

The greatest factor on the two lists that they have in common is the GCF of 17 and 14. Therefore, the GCF of 17 and 14 is 1.

In summary, the answer to the question "What is the LCM and GCF of 17 and 14?" is 238 and 1.

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