What is the LCM of 125, 25, and 5?

The least common multiple (LCM) of 125, 25, and 5 is 125.

Understanding LCM

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all the given numbers. In simpler terms, it's the smallest number that all the numbers can divide into without leaving a remainder.

Calculating the LCM of 125, 25, and 5

Here's how we can find the LCM of 125, 25, and 5:

• Prime Factorization: First, we find the prime factorization of each number:

  • 125 = 5 x 5 x 5 = 5³
  • 25 = 5 x 5 = 5²
  • 5 = 5¹

• Identify Highest Powers: Next, we look for the highest power of each prime factor present in the numbers. In this case, the only prime factor is 5. The highest power of 5 is 5³.

• Multiply Highest Powers: We then multiply these highest powers together to get the LCM. So, the LCM is 5³ = 125.

Verification

• 125 / 125 = 1
• 125 / 25 = 5
• 125 / 5 = 25

Since 125 is divisible by all three numbers (125, 25, and 5) without a remainder, and it’s the smallest number to do so, we can confirm that the LCM of 125, 25, and 5 is indeed 125, as indicated by the reference that states: "The least common multiple (LCM) of 5, 25, and 125 is 125. The LCM of two or more numbers is the smallest number that is a multiple of all of the numbers."