LCM of 24 and 90

LCM of 24 and 90 is 360. The LCM is the value evenly divisible by the numbers 24 and 90. Least common multiples of 24 and 90 can be found from the multiples which are common. (24, 48, 72, 96, 120, 144, 168, ….) and (90, 180, 270, 360, 450, 540,….) are the multiples of 24 and 90. Students will learn how to find the LCM of two numbers using prime factorization, division and by listing the multiples using the steps given in this article.

Also read: Least common multiple

What is LCM of 24 and 90?

The answer to this question is 360. The LCM of 24 and 90 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 90, is the smallest positive integer 360 which is divisible by both 24 and 90 with no remainder.

lcm of 24 and 90

How to Find LCM of 24 and 90?

LCM of 24 and 90 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 24 and 90 Using Prime Factorisation Method

The prime factorisation of 24 and 90, respectively, is given by:

24 = 2 x 2 x 2 x 3 = 2³ x 3

90 = 2 x 3 x 3 x 5 = 2¹ x 3² x 5¹

LCM (24, 90) = 360

LCM of 24 and 90 Using Division Method

We’ll divide the numbers (24, 90) by their prime factors to get the LCM of 24 and 90 using the division method (preferably common). The LCM of 24 and 90 is calculated by multiplying these divisors.

2 24 90
2 12 45
2 6 45
3 3 45
3 1 15
5 1 5
x 1 1

No further division can be done. 

Hence, LCM (24, 90) = 360

LCM of 24 and 90 Using Listing the Multiples

To calculate the LCM of 24 and 90 by listing out the common multiples, list the multiples as shown below

Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408 …..

Multiples of 90 = 90, 180, 270, 360, 450, 540, ….. 

LCM (24, 90) = 360

Related Articles

Video Lesson on Applications of LCM

LCM of 24 and 90 Solved Example 

If the product of two numbers is 2160, what is the LCM if the GCF is 6?

Solution:

It is given that

GCF = 6

Product of two numbers = 2160

LCM x GCF = Product of two numbers

LCM x 6 = 2160

LCM = 2160/6 = 360

Hence, the LCM is 360.

Frequently Asked Questions on LCM of 24 and 90

Q1

What is the LCM of 24 and 90?

The LCM of 24 and 90 is 360.
Q2

Find GCF if the LCM of 24 and 90 is 360.

LCM x GCF = 24 x 90

Given

LCM of 24 and 90 = 360

360 x GCF = 2160

GCF = 2160/360 = 6

Q3

Show the relation between GCF and LCM of 24 and 90.

The relation between GCF and LCM of 24 and 90 is

LCM x GCF = 24 x 90

LCM x GCF = 2160

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  1. 2459 and 7538 lcm

    • 2459 and 7538
      2459 is a prime number.
      Prime factorisation of 7538 = 2 × 3769
      LCM(2459, 7538) = 2 × 2459 × 3769
      = 18535942

  2. 35805 and 74074 lcm

    • 35805 and 74074
      Prime factorisation of 35805 = 3 × 5 × 7 × 11 × 31
      Prime factorisation of 74074 = 2 × 7 × 11 × 13 × 37
      LCM(35805, 74074) = 2 × 3 × 5 × 7 × 11 × 13 × 31 × 37
      = 34444410