LCM & GCF Word Problems

Front

What does LCM stand for and what does it represent?

Back

LCM stands for Least Common Multiple. It represents the smallest multiple that is exactly divisible by two or more numbers.

Front

What does GCF stand for and what does it represent?

Back

GCF stands for Greatest Common Factor. It represents the largest factor that two or more numbers share.

Front

How do you find the LCM of two numbers?

Back

To find the LCM of two numbers, list the multiples of each number and identify the smallest multiple that appears in both lists.

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How do you find the GCF of two numbers?

Back

To find the GCF of two numbers, list the factors of each number and identify the largest factor that appears in both lists.

Front

What is the relationship between LCM and GCF?

Back

The relationship is given by the formula: LCM(a, b) * GCF(a, b) = a * b for any two integers a and b.

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In the context of word problems, how can LCM be applied?

Back

LCM can be applied to determine when two or more events will coincide, such as when two people will meet at a starting point after traveling at different rates.

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In the context of word problems, how can GCF be applied?

Back

GCF can be applied to determine how to evenly distribute items into groups, such as making bouquets with the same number of flowers.

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What is an example of a real-world scenario where LCM is useful?

Back

An example is scheduling events that repeat at different intervals, such as finding out when two buses that run on different schedules will arrive at the same time.

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What is an example of a real-world scenario where GCF is useful?

Back

An example is dividing a set of items into smaller groups without leftovers, such as sharing candies among friends.

Front

How can prime factorization be used to find LCM?

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To find LCM using prime factorization, break each number down into its prime factors, then take the highest power of each prime factor present in any of the numbers.