Least Common Multiple

Front

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 using prime factorization?

Back

To find the LCM using prime factorization, first factor each number into its prime factors. Then, for each distinct prime factor, take the highest power that appears in any of the factorizations and multiply these together.

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What is the LCM of 4 and 6?

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The LCM of 4 and 6 is 12.

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What is the LCM of 9 and 15?

Back

The LCM of 9 and 15 is 45.

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What is the LCM of 18 and 27?

Back

The LCM of 18 and 27 is 54.

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What is the LCM of 20 and 30?

Back

The LCM of 20 and 30 is 60.

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What is the LCM of 10 and 25?

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The LCM of 10 and 25 is 50.

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What is the relationship between LCM and GCD (Greatest Common Divisor)?

Back

The relationship is given by the formula: LCM(a, b) = (a * b) / GCD(a, b). This means that the product of the two numbers is equal to the product of their LCM and GCD.

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Can the LCM of two numbers be smaller than either of the numbers?

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No, the LCM of two numbers is always greater than or equal to the larger of the two numbers.

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What is the LCM of three or more numbers?

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To find the LCM of three or more numbers, find the LCM of the first two numbers, then use that result to find the LCM with the next number, and continue this process.