What is the least common multiple (LCM) of two numbers?

What is the least common multiple (LCM) of two numbers?

• A. The largest number that divides both
• B. The smallest number (not zero) that is a multiple of both
• C. The sum of the two numbers
• D. The average of the two numbers

Answer: (B)

The least common multiple (LCM) of two numbers is defined as the smallest number that is a multiple of both numbers. This means that the LCM is the first number that can be evenly divided by each of the two given numbers without a remainder. For example, if we consider the numbers 4 and 6, their multiples are 4, 8, 12, 16, and so on for 4; and 6, 12, 18, 24, and so on for 6. The smallest common multiple present in both lists is 12, making it the LCM of 4 and 6. This concept helps in various applications, particularly in finding common denominators in fractions or solving problems involving periodic events. The other provided options do not correctly define the LCM: - The largest number that divides both describes the greatest common divisor (GCD), not the LCM. - The sum of the two numbers does not relate to their multiples. - The average of the two numbers is simply a measure of central tendency and does not concern multiples at all. Thus, the correct choice effectively captures the essence of what the least common multiple represents mathematically.

The least common multiple (LCM) of two numbers is defined as the smallest number that is a multiple of both numbers. This means that the LCM is the first number that can be evenly divided by each of the two given numbers without a remainder.

For example, if we consider the numbers 4 and 6, their multiples are 4, 8, 12, 16, and so on for 4; and 6, 12, 18, 24, and so on for 6. The smallest common multiple present in both lists is 12, making it the LCM of 4 and 6. This concept helps in various applications, particularly in finding common denominators in fractions or solving problems involving periodic events.

The other provided options do not correctly define the LCM:

• The largest number that divides both describes the greatest common divisor (GCD), not the LCM.

• The sum of the two numbers does not relate to their multiples.

• The average of the two numbers is simply a measure of central tendency and does not concern multiples at all.

Thus, the correct choice effectively captures the essence of what the least common multiple represents mathematically.