LCM of 36 and 63 is 252. The value of LCM is the number divisible exactly by 36 and 63. From the common multiples of 36 and 63, you will understand how the least common multiple of 36 and 63 can be calculated. The multiples of 36 are (36, 72, 108, 144, ….) and the multiples of 63 are (63, 126, 189, 252, 315, 378, ….) respectively. Division, prime factorisation and listing of the multiples are the commonly used methods to find the LCM.
Also read: Least common multiple
What is LCM of 36 and 63?
The answer to this question is 252. The LCM of 36 and 63 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 63, is the smallest positive integer 252 which is divisible by both 36 and 63 with no remainder.
How to Find LCM of 36 and 63?
LCM of 36 and 63 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 63 Using Prime Factorisation Method
The prime factorisation of 36 and 63, respectively, is given by:
36 = 2 × 2 × 3 × 3 = 2²× 3²
63 = 3 × 3 × 7 = 3² × 7¹
LCM (36, 63) = 252
LCM of 36 and 63 Using Division Method
We’ll divide the numbers (36, 63) by their prime factors to get the LCM of 36 and 63 using the division method (preferably common). The LCM of 36 and 63 is calculated by multiplying these divisors.
| 2 | 36 | 63 |
| 2 | 18 | 63 |
| 3 | 9 | 63 |
| 3 | 3 | 21 |
| 7 | 1 | 7 |
| × | 1 | 1 |
No further division can be done.
Hence, LCM (36, 63) = 252
LCM of 36 and 63 Using Listing the Multiples
To calculate the LCM of 36 and 63 by listing out the common multiples, list the multiples as shown below
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, . . . .
Multiples of 63 = 63, 126, 189, 252, 315, 378, 441, . . . .
LCM (36, 63) = 252
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Video Lesson on Applications of LCM
LCM of 36 and 63 Solved Examples
Question: If the product of two numbers is 2268, find the LCM if the GCD is 9.
Solution:
It is given that
GCD = 9
Product of two numbers = 2268
We know that
LCM × GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 2268/9
LCM = 252
Hence, the LCM is 252.
Frequently Asked Questions on LCM of 36 and 63
What is the LCM of 36 and 63?
If the LCM of 36 and 63 is 252, what is the GCF?
LCM × GCF = 36 × 63
Given;
LCM of 36 and 63 is 252
252 × GCF = 2268
GCF = 2268/252 = 9
List the methods used to find the LCM of 36 and 63.
The methods used to find the LCM of 36 and 63 are:
Division method
Prime Factorisation
Listing the multiples
The LCM and GCD of two numbers are 252 and 9. If one number is 36, find the other.
Consider x as the other number
GCD × LCM = 36 × x
x = (GCD × LCM)/36
x = (9 × 252)/36
x = 63
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