What is the definition of a least common multiple (LCM)?

What is the definition of a least common multiple (LCM)?

• A. The smallest non-zero number that is a multiple of two or more numbers
• B. The greatest number that divides two or more numbers
• C. The sum of two or more numbers
• D. The product of two or more numbers

Answer: (A)

The least common multiple (LCM) is defined as the smallest non-zero number that is a multiple of two or more numbers. This concept is crucial in various areas of mathematics, particularly in solving problems related to fractions, ratios, and timing issues where events repeat at different intervals. When finding the LCM, we are essentially looking for the smallest number that both (or all) of the given numbers can divide evenly into without any remainder. For example, if you consider the numbers 4 and 5, the multiples of 4 are 4, 8, 12, 16, 20, etc., and the multiples of 5 are 5, 10, 15, 20, etc. The smallest number that appears in both lists is 20, making it the LCM of 4 and 5. In contrast, the other options do not accurately describe the LCM. The greatest number that divides two or more numbers refers to the greatest common divisor (GCD). The sum is simply the result of adding numbers together, and the product refers to the result of multiplying them. Therefore, option A accurately captures the essence of what the LCM is.

The least common multiple (LCM) is defined as the smallest non-zero number that is a multiple of two or more numbers. This concept is crucial in various areas of mathematics, particularly in solving problems related to fractions, ratios, and timing issues where events repeat at different intervals.

When finding the LCM, we are essentially looking for the smallest number that both (or all) of the given numbers can divide evenly into without any remainder. For example, if you consider the numbers 4 and 5, the multiples of 4 are 4, 8, 12, 16, 20, etc., and the multiples of 5 are 5, 10, 15, 20, etc. The smallest number that appears in both lists is 20, making it the LCM of 4 and 5.

In contrast, the other options do not accurately describe the LCM. The greatest number that divides two or more numbers refers to the greatest common divisor (GCD). The sum is simply the result of adding numbers together, and the product refers to the result of multiplying them. Therefore, option A accurately captures the essence of what the LCM is.