LCM of 6 and 9

LCM (Least Common Multiple) of two numbers is the smallest multiple that both numbers can divide evenly without leaving any remainder.

In this article, we will learn about LCM, What is LCM of 6 and 9, How to Find LCM of 6 and 9, LCM of 6 and 9 by Prime Factorization, Listing Multiples, and by Long Division. We will also look into comparison of LCM vs HCF of 6 and 9 in detail.

What is LCM of 6 and 9?

Answer: LCM of 6 and 9 is 18

LCM of any set of numbers is the smallest number that is divisible by each of the numbers in the set without leaving a remainder. Now, focusing on the numbers 6 and 9, we aim to find their LCM, which is the smallest number divisible by both 6 and 9. In simpler terms, it’s the smallest multiple that these numbers have in common. After careful calculation, we determine that the LCM of 6 and 9 is 18.

LCM of 6 and 9 Calculator

Try out the following calculator to find the LCM of 6 and 9

How to Find LCM of 6 and 9?

There are several methods to find the LCM of two numbers. Here, we will discuss three commonly used approaches:

• Prime Factorization
• Listing Multiples
• Division

LCM of 6 and 9 by Prime Factorization

This method involves breaking down each number into its prime factors and then determining the product of the highest powers of all the prime factors. We’ll illustrate this method in detail in the subsequent section.

On Prime factorization

• 6 = 2 × 3
• 9 = 3 × 3

Here, 2 appears once and 3 appears twice.

So LCM = 2 × 3 × 3 = 18

LCM of 6 and 9 by Listing Multiples

In this method, we list the multiples of each number until we find a common multiple. We continue listing until we identify the smallest multiple shared by both numbers. This method provides a straightforward approach to finding the LCM.

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54 . . .

Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81 . . .

The common multiples of 6 and 9 are 18, 36, 54 . . .

Among these 18 is the lowest common multiple

So, LCM of 6 and 9 = 18

LCM of 6 and 9 by Division

Long division is another method to determine the LCM. We divide the larger number by the smaller number, and then we continue dividing the result by the Greatest Common Divisor of the two numbers until we reach a quotient of 1. The product of all the divisors used in this process gives us the LCM. LCM of 6 and 9 by division method is shown below:

LCM of 6 and 9 by Division Method

LCM vs HCF of 6 and 9

When we compare the LCM (Least Common Multiple) and HCF (Highest Common Factor) of two numbers 6 and 9 we have the following observations:

LCM of 6 and 9	HCF of 6 and 9
LCM would be the smallest number that both 6 and 9 can evenly divide into without the remainder.	HCF is the biggest number that can divide both 6 and 9, leaving no remainder.
LCM of 6 and 9 is 18	LCM of 6 and 9 is 3
LCM is the common multiple greater than or equal to 18	HCF is the common factor less than or equal to 12

Examples on LCM of 6 and 9

Example 1: Find the sum of the LCM and HCF of 6 and 9.

Solution:

LCM(6, 9) = 18

HCF(6, 9) = 3

Sum = LCM + HCF = 18 + 3 = 21

Example 2: Find the product of the LCM and HCF of 6 and 9.

Solution:

LCM(6, 9) = 18

HCF(6, 9) = 3

Product = LCM × HCF = 18 × 3 = 54

Example 3: Find the difference between the LCM and HCF of 6 and 9.

Solution:

LCM(6, 9) = 18

HCF(6, 9) = 3

Difference = LCM – HCF = 18 – 3 = 15

LCM of 6 and 9 Practice Problems

Q1. What is the product of all the factors of 54?

Q2. Two plants are irrigated at every 6 and 9 days. On which day they will be irrigated together?

Q3. If HCF and LCM of two numbers is 3 and 18 respectively. If one number is 6, find the other number.

Q4. Find the LCM of 6 and 9 by Prime Factorization method.

LCM of 6 and 9 Frequently Asked Questions

What does LCM stand for?

LCM stands for Least Common Multiple.

What is LCM of 6 and 9?

LCM of 6 and 9 is 18

How can I find the LCM of 6 and 9?

You can find the LCM of 6 and 9 by listing out their multiples and identifying the smallest number they have in common. Alternatively, you can use methods like prime factorization or long division.

Can you find the LCM of more than two numbers?

Yes, you can find the LCM of more than two numbers. The process is similar to finding the LCM of two numbers, but you’ll need to consider all the numbers involved.

What is the relationship between LCM and HCF?

LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers, while HCF (Highest Common Factor) is the largest number that divides both numbers evenly. The product of LCM and HCF is equal to the product of the two numbers.

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

No, the LCM of two numbers must always be greater than or equal to both numbers.

Can LCM be negative?

No, LCM is always a positive number because it represents the smallest positive multiple that two or more numbers share.

What is HCF of 6 and 9?

HCF of 6 and 9 is 3