LCM of 42 and 54 is 378. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. All common multiples of 42 and 54 have an LCM of 42 and 54, which is the smallest number. (42, 84, 126, 168, 210, etc.) and (54, 108, 162, 216, etc.) are the first few multiples of 42 and 54.
Also read: Least common multiple
What is LCM of 42 and 54?
The answer to this question is 378. The LCM of 42 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 42 and 54, is the smallest positive integer 378 which is divisible by both 42 and 54 with no remainder.
How to Find LCM of 42 and 54?
LCM of 42 and 54 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 42 and 54 Using Prime Factorisation Method
The prime factorisation of 42 and 54, respectively, is given by:
42 = (2 × 3 × 7) = 21 × 31 × 71 and
54 = (2 × 3 × 3 × 3) = 21 × 33
LCM (42, 54) = 378
LCM of 42 and 54 Using Division Method
We’ll divide the numbers (42, 54) by their prime factors to get the LCM of 42 and 54 using the division method (preferably common). The LCM of 42 and 54 is calculated by multiplying these divisors.
| 2 | 42 | 54 |
| 3 | 21 | 27 |
| 3 | 7 | 9 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (42, 54) = 378
LCM of 42 and 54 Using Listing the Multiples
To calculate the LCM of 42 and 54 by listing out the common multiples, list the multiples as shown below.
| Multiples of 42 | Multiples of 54 |
| 42 | 54 |
| 84 | 108 |
| 126 | 162 |
| ……. | …… |
| 378 | 378 |
The smallest common multiple of 42 and 54 is 378.
Therefore LCM (42, 54) = 378
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LCM of 42 and 54 Solved Example
The product of two numbers is 2268. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 2268
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2268/6
Therefore, the LCM is 378.
The probable combination for the given case is LCM(42, 54) = 378.
Frequently Asked Questions on LCM of 42 and 54
What is the LCM of 42 and 54?
List the methods used to find the LCM of 42 and 54.
Which of the following is the LCM of 42 and 54? 3, 25, 42, 378
If the LCM of 54 and 42 is 378, Find its GCF.
Since the LCM of 54 and 42 = 378
⇒ 378 × GCF(54, 42) = 2268
Therefore, the greatest common factor = 2268/378 = 6.
How to Find the LCM of 42 and 54 by Prime Factorization?
⇒ LCM of 42, 54 = 2 × 33 × 7 = 378.
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