LCM of 27 and 63 is 189. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Least common multiple of 27 and 63 is the smallest number among all common multiples of 27 and 63. The first few multiples of 27 and 63 are (27, 54, 81, 108, 135, . . . ) and (63, 126, 189, 252, 315, 378, 441, . . . ) 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 27 and 63?
The answer to this question is 189. The LCM of 27 and 63 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 27 and 63, is the smallest positive integer 189 which is divisible by both 27 and 63 with no remainder.
How to Find LCM of 27 and 63?
LCM of 27 and 63 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 27 and 63 Using Prime Factorisation Method
The prime factorisation of 27 and 63, respectively, is given by:
27 = (3 × 3 × 3) = 33 and
63 = (3 × 3 × 7) = 32 × 71
LCM (27, 63) = 189
LCM of 27 and 63 Using Division Method
We’ll divide the numbers (27, 63) by their prime factors to get the LCM of 27 and 63 using the division method (preferably common). The LCM of 27 and 63 is calculated by multiplying these divisors.
| 3 | 27 | 63 |
| 3 | 9 | 21 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
No further division can be done.
Hence, LCM (24, 36) = 72
LCM of 27 and 63 Using Listing the Multiples
To calculate the LCM of 27 and 63 by listing out the common multiples, list the multiples as shown below
| Multiples of 27 | Multiples of 63 |
| 27 | 63 |
| 54 | 126 |
| 81 | 189 |
| ….. | 252 |
| 189 | 315 |
The smallest common multiple of 27 and 63 is 189.
Therefore LCM (27, 63) = 189
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LCM of 27 and 63 Solved Example
The product of two numbers is 1701. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 1701
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1701/9
Therefore, the LCM is 189.
The probable combination for the given case is LCM(27, 63) = 189.
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