LCM and GCF

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What is the least common multiple (LCM)?

Back

The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the integers.

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How do you find the LCM of two numbers?

Back

To find the LCM of two numbers, you can use the prime factorization method, listing the multiples, or using the formula: LCM(a, b) = (a * b) / GCF(a, b).

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor (GCF) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.

Front

How do you find the GCF of two numbers?

Back

To find the GCF of two numbers, you can use the prime factorization method, listing the factors, or using the Euclidean algorithm.

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What are multiples of a number?

Back

Multiples of a number are the products of that number and any integer. For example, the multiples of 5 are 5, 10, 15, 20, etc.

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What are factors of a number?

Back

Factors of a number are the integers that can be multiplied together to produce that number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

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What is the relationship between LCM and GCF?

Back

The relationship between LCM and GCF is given by the formula: LCM(a, b) * GCF(a, b) = a * b.

Front

If Lisa has 12 coloring books and 36 crayons, how do you determine the maximum number of baskets she can make?

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To determine the maximum number of baskets, find the GCF of 12 and 36, which is 12. This means she can make 12 baskets with an equal distribution.

Front

What is an example of finding the LCM using prime factorization?

Back

To find the LCM of 4 and 10 using prime factorization: 4 = 2^2, 10 = 2^1 * 5^1. The LCM is 2^2 * 5^1 = 20.

Front

What is an example of finding the GCF using prime factorization?

Back

To find the GCF of 12 and 18 using prime factorization: 12 = 2^2 * 3^1, 18 = 2^1 * 3^2. The GCF is 2^1 * 3^1 = 6.