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what is the least common multiple of 8 and 12

Grade 6 Math Worksheets

The lowest common multiple (LCM) is the smallest multiple that two or more numbers have in common. In other words, it’s the smallest positive number divisible by both (or all) of the given numbers without leaving a remainder.

List of Contents:

  • How to Find LCM of 8 and 12?
  • Prime Factorization
  • Listing the multiples
  • Division method
  • FAQs

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what is the least common multiple of 8 and 12 - Grade 6 Math Worksheet PDF

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How to Find LCM of 8 and 12?

The lowest common multiple (LCM) is the smallest multiple that two or more numbers have in common. In other words, it’s the smallest positive number divisible by both (or all) of the given numbers without leaving a remainder.

LCM of 8 and 12 can be determined using three methods:

  • Prime Factorization
  • Division method
  • Listing the multiples

Prime Factorization

Let’s find the least common multiple (LCM) of 8 and 12 using the prime factorization method,

Step 1: Write down the two numbers, 8 and 12, for which you want to find the LCM.

Step 2: Find the prime factors of each number.

Prime factors of 8:
8 can be divided by 2, giving a quotient of 4.
4 can be divided by 2, giving a quotient of 2.
2 can be divided by 2, giving a quotient of 1.
So, the prime factorization of 8 is 2 × 2 × 2, which can also be written as 23

Prime factors of 12:
12 can be divided by 2, giving a quotient of 6.
6 can be divided by 2, giving a quotient of 3.
3 can’t be divided any further.
So, the prime factorization of 12 is 2 × 2 × 3, which can also be written as 22× 3.

Step 3: Multiply the highest powers of each prime factor.
The highest power is 23 from the prime factorization of 8.
The highest power is 31 from the prime factorization of 12
23× 31 = 8 × 3 = 24.

So, the least common multiple of 8 and 12 is 24

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Listing the Multiples

LCM of 8 and 12 Using Listing the Multiples
List the multiples of 8 and 12 until you find a common multiple.

Multiples of 8: 8, 16, 24, 32, 40, …
Multiples of 12: 12, 24, 36, 48, …

You can see that the first common multiple of 8 and 12 is 24.
So, the least common multiple of 8 and 12 is 24

 

least common multiple

 

Division Method

LCM of 8 and 12 Using Division Method

In the Division Method, the given numbers are written in the same row.

These numbers are divided with the smallest number that divides all until no further division is possible or only when prime numbers are left.

Then, we multiply the numbers on the left.
So, the least common multiple of 8 and 12 is 24

 

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what is the least common multiple of 8 and 12 FAQS

What is the LCM of 8 and 12?

The LCM of 8 and 12 is 24. It’s the smallest multiple that both 8 and 12 share.

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

 No, the LCM of two numbers is always equal to or greater than the largest number among them. 

LCM of 8 and 12 is the same as the LCM of 4 and 8?

No, LCM of 8 and 12 is 24, and LCM of 4 and 8 is 8. They are not the same.

Is the LCM unique for any two given numbers?

Yes, the LCM is unique for any two given numbers. While there can be multiple common multiples, the least common multiple (LCM) is the smallest among them and is unique for those two numbers.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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