LCM of 36 and 84 is 252.The smallest number among all common multiples of 36 and 84 is the LCM of 36 and 84. (36, 72, 108, 144, 180, 216, 252, etc.) and (84, 168, 252, 336, 420, 504, 588, etc.) are the first few multiples of 36 and 84, respectively. To get the LCM of 36 and 84, there are three main methods: prime factorization, division method, and listing multiples. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 36 and 84?
The answer to this question is 252. The LCM of 36 and 84 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 84, is the smallest positive integer 252 which is divisible by both 36 and 84 with no remainder.
How to Find LCM of 36 and 84?
LCM of 36 and 84 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 84 Using Prime Factorisation Method
The prime factorisation of 36 and 84, respectively, is given by:
36 = (2 × 2 × 3 × 3) = 22 × 32 and
84 = (2 × 2 × 3 × 7) = 22 × 31 × 71
LCM (36, 84) = 252
LCM of 36 and 84 Using Division Method
We’ll divide the numbers (36, 84) by their prime factors to get the LCM of 36 and 84 using the division method (preferably common). The LCM of 36 and 84 is calculated by multiplying these divisors.
| 2 | 36 | 84 |
| 2 | 18 | 42 |
| 3 | 9 | 21 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (36, 84) = 252
LCM of 36 and 84 Using Listing the Multiples
To calculate the LCM of 36 and 84 by listing out the common multiples, list the multiples as shown below
| Multiples of 36 | Multiples of 84 |
| 36 | 84 |
| 72 | 168 |
| 108 | 252 |
| 144 | 336 |
| 180 | 420 |
| 216 | – |
| 252 | – |
The smallest common multiple of 36 and 84 is 252.
Therefore LCM (36, 84) = 252
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LCM of 36 and 84 Solved Example
Question: The GCD and LCM of two numbers are 12 and 252 respectively. If one number is 84, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 84 × y
⇒ y = (GCD × LCM)/84
⇒ y = (12 × 252)/84
⇒ y = 36
Therefore, the other number is 36.
Frequently Asked Questions on LCM of 36 and 84
What is the LCM of 36 and 84?
List the methods used to find the LCM of 36 and 84.
If the LCM of 84 and 36 is 252, Find its GCF.
Since the LCM of 84 and 36 = 252
⇒ 252 × GCF(84, 36) = 3024
Therefore, the greatest common factor = 3024/252 = 12.
What is the Least Perfect Square Divisible by 36 and 84?
LCM of 36 and 84 = 2 × 2 × 3 × 3 × 7 [Incomplete pair(s): 7] ⇒ Least perfect square divisible by each 36 and 84 = LCM(36, 84) × 7 = 1764 [Square root of 1764 = √1764 = ±42] Therefore, 1764 is the required number.
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