LCM of 36 and 48 is 144. The common multiples of the numbers 36 and 48 which are divisible evenly by the given numbers is the LCM. Least common multiples of 36 and 48 can be determined from the common multiples of the numbers given. (36, 72, 108, 144, 180, 216, ….) and (48, 96, 144, 192, 240, 288,….) are the multiples of 36 and 48. You can make use of methods such as division, prime factorisation and listing of multiples to obtain the LCM.
Also read: Least common multiple
What is LCM of 36 and 48?
The answer to this question is 144. The LCM of 36 and 48 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 48, is the smallest positive integer 144 which is divisible by both 36 and 48 with no remainder.
How to Find LCM of 36 and 48?
LCM of 36 and 48 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 48 Using Prime Factorisation Method
The prime factorisation of 36 and 48, respectively, is given by:
36 = 2 x 2 x 3 x 3 = 2² x 3²
48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3¹
LCM (36, 48) = 144
LCM of 36 and 48 Using Division Method
We’ll divide the numbers (36, 48) by their prime factors to get the LCM of 36 and 48 using the division method (preferably common). The LCM of 36 and 48 is calculated by multiplying these divisors.
| 2 | 36 | 48 |
| 2 | 18 | 24 |
| 2 | 9 | 12 |
| 2 | 9 | 6 |
| 3 | 9 | 3 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (36, 48) = 144
LCM of 36 and 48 Using Listing the Multiples
To calculate the LCM of 36 and 48 by listing the common multiples, list the multiples as shown below.
| Multiples of 36 | Multiples of 48 |
| 36 | 48 |
| 72 | 96 |
| 108 | 144 |
| 144 | 192 |
LCM (36, 48) = 144
Related Articles
Video Lesson on Applications of LCM
LCM of 36 and 48 Solved Example
Question: Find the LCM if the product of two numbers is 1728 and the GCD is 12.
Solution:
It is given that
Product of two numbers = 1728
GCD = 12
We know that;
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 1728/12
LCM = 144
Hence, the LCM is 144.
Frequently Asked Questions on LCM of 36 and 48
Determine the LCM of 36 and 48.
List the methods used to determine the LCM of 36 and 48.
What is the GCF if the LCM of 36 and 48 is 144?
LCM x GCF = 36 x 48
Given
LCM of 36 and 48 = 144
144 x GCF = 1728
GCF = 1728/144 = 12
Comments