Least Common Multiple of 6 and 9

Grade 6 Math Worksheets

The least common multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both of those numbers.

In other words, the smallest positive integer is a multiple of the given numbers. LCM of 6 and 9 is the smallest number that can be evenly divided by both 6 and 9.

In this article, we will cover:

LCM of 6 and 9
Methods to Find LCM of 6 and 9
By Prime Factorization Method
By Listing Multiples
By Division Method
Solved Examples
FAQs

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Least Common Multiple of 6 and 9 - Grade 6 Math Worksheet PDF

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What is the LCM of 6 and 9?

LCM of 6 and 9 is 18.

Explanation: The least common multiple (LCM) of two non-zero integers (in this case, 6 and 9) is the smallest positive integer (18) that is divisible by both 6 and 9 without any remainder. In other words, it’s the smallest common multiple that both numbers share.

Methods to Find LCM of 6 and 9

Let’s look at the different methods for finding the LCM of 6 and 9.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 6 and 9 by Listing Multiples

Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, 42, . . . ) and 9 (9, 18, 27, 36, 45, 54, . . . )
Step 2: The common multiples from the multiples of 6 and 9 are 18, 36, . . .
Step 3: Find the smallest common multiple of 6 and 9, and it is 18.

The least common multiple of 6 and 9 is 18.

LCM of 6 and 9 by Prime Factorization

Step 1: Prime factorize both 6 and 9

6: 2 × 3 = 21 × 31
9: 3 × 3 = 32

Step 2: Identify the Highest Powers of Prime Factors

Highest power of 2: 21 (from 6)
Highest power of 3: 32 (from 9)

Step 3: Multiply the Highest Powers

21× 32 = 2 × 9 = 18

The LCM of 6 and 9 is 18.

LCM of 6 and 9 by Division Method

In this method, we divide the numbers 6 and 9 by their prime factors to find their LCM. The product of these divisors denotes the least common multiple of 6 and 9.

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LCM of 6 and 9 Examples

Question 1: The product of two numbers is 70. If their GCD is 5, what is their LCM?

Solution: Use the formula

Product of two numbers=GCD×LCM

Substituting the given values (product = 70, GCD = 5):

70= 5 × LCM

Now, solve for the LCM:

LCM = 70/5 = 14

The LCM of the two numbers is 14.

Question 2: Find the smallest number divisible by 6 and 9 exactly.

Solution: The smallest number that is divisible by 6 and 9 exactly is their LCM.

Question 3: What are the methods to find LCM of 6 and 9?

Solution: The commonly used methods to find LCM of 6 and 9 are the prime factorization method, listing multiples, and division method.

Question 4: Are LCM and GCF identical for 6 and 9?

Solution: No, the least common multiple (LCM) and greatest common factor (GCF) are not the same for the numbers 6 and 9.

The LCM of two numbers is the smallest multiple that is evenly divisible by both of those numbers.

The GCF of two numbers is the largest positive integer that divides both of those numbers without leaving a remainder.

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FAQs

What is the LCM of 6 and 9?

The LCM of 6 and 9 is the smallest multiple that is evenly divisible by both 6 and 9. In this case, the LCM is 18.

How do you find the LCM of 6 and 9?

To find the LCM of 6 and 9, you can use various methods, including prime factorization, listing multiples, or using the method of finding the greatest common divisor (GCD) and then using the formula: LCM(a, b) = (a * b) / GCD(a, b).

What are the multiples of 6 and 9?

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, and so on. The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, and so on.

Why is 18 the LCM of 6 and 9?

The LCM is the smallest common multiple of two numbers. In this case, 18 is the smallest number that both 6 and 9 can divide evenly. The smallest number is a multiple of both 6 and 9.

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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