LCM of 36 and 96 is 288. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 36 and 96 is the smallest number among all common multiples of 36 and 96. The first few multiples of 36 and 96 are (36, 72, 108, 144, . . . ) and (96, 192, 288, 384, 480, 576, . . . ) respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 36 and 96?
The answer to this question is 288. The LCM of 36 and 96 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 96, is the smallest positive integer 288 which is divisible by both 36 and 96 with no remainder.
How to Find LCM of 36 and 96?
LCM of 36 and 96 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 96 Using Prime Factorisation Method
The prime factorisation of 36 and 96, respectively, is given by:
36 = (2 × 2 × 3 × 3) = 22 × 32 and
96 = (2 × 2 × 2 × 2 × 2 × 3) = 25 × 31
LCM (36, 96) = 288
LCM of 36 and 96 Using Division Method
We’ll divide the numbers (36, 96) by their prime factors to get the LCM of 36 and 96 using the division method (preferably common). The LCM of 36 and 96 is calculated by multiplying these divisors.
| 2 | 36 | 96 |
| 2 | 18 | 48 |
| 2 | 9 | 24 |
| 2 | 9 | 12 |
| 2 | 9 | 6 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (36, 96) = 288
LCM of 36 and 96 Using Listing the Multiples
To calculate the LCM of 36 and 96 by listing out the common multiples, list the multiples as shown below
| Multiples of 36 | Multiples of 96 |
| 36 | 96 |
| 72 | 192 |
| 108 | 288 |
| …… | 384 |
| 288 | 480 |
The smallest common multiple of 36 and 96 is 288.
Therefore LCM (36, 96) = 288
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LCM of 36 and 96 Solved Example
The GCD and LCM of two numbers are 12 and 288 respectively. If one number is 96, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 96 × m
⇒ m = (GCD × LCM)/96
⇒ m = (12 × 288)/96
⇒ m = 36
Therefore, the other number is 36.
Frequently Asked Questions on LCM of 36 and 96
What is the LCM of 36 and 96?
List the methods used to find the LCM of 36 and 96.
If the LCM of 96 and 36 is 288, Find its GCF.
Since the LCM of 96 and 36 = 288
⇒ 288 × GCF(96, 36) = 3456
Therefore, the GCF (greatest common factor) = 3456/288 = 12.
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