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LCM of 3 and 9

LCM of 3 and 9 is 9. The number evenly divisible by the given numbers provides the LCM. From the multiples which are common, the least common multiple of 3 and 9 can be found. The multiples of 3 are (3, 6, 9, 12, 15, 18, 21, ….) and the multiples of 9 are (9, 18, 27, 36, 45, 54, ….) respectively. The methods used to calculate the LCM are prime factorisation, division and by listing the multiples.

Also read: Least common multiple

What is LCM of 3 and 9?

The answer to this question is 9. The LCM of 3 and 9 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 9, is the smallest positive integer 9 which is divisible by both 3 and 9 with no remainder.

lcm of 3 and 9

How to Find LCM of 3 and 9?

LCM of 3 and 9 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 3 and 9 Using Prime Factorisation Method

The prime factorisation of 3 and 9, respectively, is given by:

3 = 3¹ 

9 = 3 x 3 = 3²

LCM (3, 9) = 9

LCM of 3 and 9 Using Division Method

We’ll divide the numbers (3, 9) by their prime factors to get the LCM of 3 and 9 using the division method (preferably common). The LCM of 3 and 9 is calculated by multiplying these divisors.

3 3 9
3 1 3
1 1

No further division can be done. 

Hence, LCM (3, 9) = 9

LCM of 3 and 9 Using Listing the Multiples

To calculate the LCM of 3 and 9 by listing out the common multiples, list the multiples as shown below

Multiples of 3 Multiples of 9
3 9
6 18
9 27
12 36
15 45

LCM (3, 9) = 9

Related Articles

Video Lesson on Applications of LCM

LCM of 3 and 9 Solved Examples 

The LCM and GCD of two numbers are 9 and 3 respectively. If one number is 9, what is the other number?

Solution:

Consider the number as z

We know that

GCD x LCM = 9 x z

z = (GCD x LCM)/9

Substituting the values

z = (9 x 3)/9

z = 3

Hence, the other number is 3.

Frequently Asked Questions on LCM of 3 and 9

If the LCM of 3 and 9is 9, what is its GCF?

We know that

LCM x GCF = 3 x 9

As LCM (3, 9) is 9

9 x GCF = 27

GCF = 27/9 = 3

Find the LCM of 3 and 9.

The LCM of 3 and 9 is 9. To find the LCM, we first should understand the multiples of 3 and 9

Multiples of 3 = 3, 6, 9, 12, 15, 18, ……

Multiples of 9 = 9, 18, 27, 36, 45, 54, ….

The smallest multiple exactly divisible by 3 and 9 is 9.

Show the relation between GCF and LCM of 3 and 9.

The relation between GCF and LCM of 3 and 9 is

LCM x GCF = 3 x 9

LCM x GCF = 27

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