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.
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
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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
What is the LCM of 24 and 90?
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
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
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
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