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Last updated on November 29th, 2024

LCM of 6 and 15

Q: What is the HCF of 6 and 15?

Factors of 6: 1,2,3,6 Factors of 15: 1,3,5,15 The common factors of 6 and 15 are 1 and 3, and the greatest of them is 3. The HCF of 6,15 = 3

Q: What is the LCM of 6,15 and 12?

LCM (6,15,12) = 60 60 is the smallest number that appears commonly on the lists of the numbers 6,12 and 15.

Q: Find the prime factors of each number:

Prime factorization of 6 =2×3 Prime factorization of 12 = 2×2×3 Prime factorization of 15 =5×3

Q: What is the highest multiple of 6 and 15?

There, technically, can be no highest multiple as multiples continue infinitely. However, the LCM of 6 and 15 is 30, after which their shared multiple is 60,90,120 and so on.

Q: What are the factors of 15?

Factors of 15: 1,3,5,15. Numbers that are multiplied to reach 15 are called the factors.

Professor Greenline Explaining Math Concepts

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Advance Topics

LCM is a common multiple, the smallest value between the numbers 6 and 15. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.

What is the LCM of 6 and 15?

The LCM of 6 and 15 is 30. We can find the LCM using the Listing multiples method, the prime factorization method and the long division method. These are explained below.

LCM of 6 abd 15 Using Listing the Multiples

Step 1: Write down the multiples of the numbers. Don’t stop too early.

Multiples of 6 = 6,12,18,24,30,36, …

Multiples of 15 = 15,30,45,60,75,…

Step 2: Find the smallest number common between the written multiples of 3 and 8

The smallest common multiple is 30

Thus, LCM(6,15) = 30

LCM of 6 and 15 Using Prime Factorization

Step 1:factorize the numbers into its prime factors

6 = 3×2

15 = 3×5

Step 2: find the highest powers of the factors of 6 and 15

Step 3: Multiply the highest powers

LCM (6,15) = 30

LCM of 6 and 15 Using Division Method

Write the numbers 6,15 in a row

Divide them by their common prime factors, if there is one

Carry forward the numbers that are left undivided by the previously chosen factor

Continue dividing until the remainder is ‘1’

Multiply the divisors to find the LCM

LCM(6,15) = 30

Common Mistakes and how to avoid them while finding the LCM of 6 and 15

LCM of 6 and 15 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

The LCM of 6 and a number x is 30. Find x.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

Problem 2

Use the relationship LCM(a,b)×GCF(a,b)=a×b to verify the LCM of 6 and 15.

Explanation

Problem 3

Simplify the sum 1/6+1/15 using the LCM of the denominators.

Explanation

FAQs on LCM of 6 and 15

1.What is the HCF of 6 and 15?

2.What is the LCM of 6,15 and 12?

3.Find the prime factors of each number:

4.What is the highest multiple of 6 and 15?

5.What are the factors of 15?

Important glossaries on the LCM of 6 and 15

Multiple — product of a number and a natural integer

Prime factor — number one gets after prime factorization any given number

Prime factorization — the process of breaking the number into its prime factors.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.