Least Common Multiple for 4 and 6

Grade 6 Math Worksheets

The least common multiple (LCM) of two numbers is the smallest positive integer divisible by both numbers. So, the LCM of 4 and 6 is the smallest positive number among all common multiples of 4 and 6.

In this article, we will cover:

LCM of 4 and 6
How to Find LCM of 4 and 6
By Prime Factorization Method
By Listing Multiples
By Division Method
Examples
FAQs

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Least Common Multiple for 4 and 6 - Grade 6 Math Worksheet PDF

This is a free printable / downloadable PDF worksheet with practice problems and answers. You can also work on it online.

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LCM of 4 and 6

LCM of 4 and 6 is 12.

Explanation: The least common multiple (LCM) of two non-zero integers (in this case, 4 and 6) is the smallest positive integer (12) that is divisible by both 4 and 6 without any remainder. In other words, it’s the smallest common multiple that both numbers share.

How to Find LCM of 4 and 6?

Methods for finding the Least Common Multiple of 4 and 6:

By Prime Factorization Method
By Listing Multiples
By Division Method

By Listing Multiples

Step 1: write out some multiples of 4: 4, 8, 12, 16, 20, 24, 28, …Multiples of 6: 6, 12, 18, 24, 30, 36, …
Step 2: Find out common multiples from the multiples of 4 and 6
Step 3: It can be observed that 12 represents the minimum common multiple of 4 and 6.

By Prime Factorization

Step 1: Prime factorize both 4 and 6

4: 2 × 2 = 22
6: 2 × 3 = 21 × 31

Step 2: Identify the Highest Powers of Prime Factors

Highest power of 2: 22 (from 4)
Highest power of 3: 31 (from 6)

Step 3: Multiply the Highest Powers

22× 31 = 4 × 3 = 12

The least common multiple (LCM) between 4 and 6 equals 12.

By Division Method

In this method, we divide the numbers 4 and 6 by their prime factors to find their LCM. The product of these divisors denotes the least common multiple of 4 and 6.

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LCM of 4 and 6 Examples

Example 1: The product of two numbers is 24. If their GCD is 2, what is their LCM?The product of two numbers is 42, and their GCD is 7. What is their LCM?

Given that the product of two numbers is 42 and their greatest common divisor (GCD) is 7, we can use the relationship between the GCD and LCM:

GCD×LCM=Product of the numbers

Substitute the given values:

7×LCM=42

Now, solve for the LCM

LCM=42/7=6

So, the two numbers’ least common multiple (LCM) is 6.

Example 2: If one of the two numbers is 6, and their greatest common divisor (GCD) is 2, while their least common multiple (LCM) is 24, what is the value of the other number?

Given that the greatest common divisor (GCD) of two numbers is 2 and the least common multiple (LCM) is 24, and you know that one of the numbers is 6, you can find the other number using the relationship between GCD, LCM, and the product of the two numbers.

GCD×LCM=Product of the numbers

Substitute the given values:

2×24=6×Other number

Now, solve for the other number:

Other number=2×24/6 = 8

So, the other number is 8.

Example 3: Find the smallest number divisible by 4 and 6.

The smallest number that is divisible by 4 and 6 is their LCM.

Multiples of 4 (4, 8, 12, 16, 20, 24, 28, . . . )

Multiples of 6 (6, 12, 18, 24, 30, 36, 42, . . . )

The smallest common multiple of 6 and 8 is 24.

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FAQs

What is the LCM of 4 and 6?

The LCM of 4 and 6 is the smallest multiple that is evenly divisible by both 4 and 6. In this case, the LCM is 12.

What are the multiples of 4 and 6?

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, and so on. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, and so on.

Why is 12 the LCM of 4 and 6?

The LCM is the smallest common multiple of two numbers. In this case, 12 is the smallest number that both 4 and 6 can evenly divide. The smallest number is a multiple of both 4 and 6.

What is the relationship between LCM and GCD?

The LCM (Least Common Multiple) and the GCD (Greatest Common Divisor) are related by the formula: LCM(a, b) = (a * b) / GCD(a, b). In this case, for 4 and 6, LCM(4, 6) = (4 * 6) / GCD(4, 6), which simplifies to LCM(4, 6) = 24 / 2 = 12.

Why is the LCM important in mathematics?

The LCM is essential in various mathematical applications, such as solving equations, simplifying fractions, and working with proportions. It helps find a common denominator when adding or subtracting fractions and is crucial in number theory.

Is the LCM always greater than or equal to the original numbers?

Yes, the LCM is always greater than or equal to the original numbers. The smallest number is a multiple of both numbers, so it must be at least as large as the largest of the two numbers.

Can you find the LCM of more than two numbers?

Yes, you can find the LCM of more than two numbers. The process involves finding the LCM of pairs of numbers sequentially or using prime factorization for multiple 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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