LCM of 42 and 48 is 336. 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. LCM of 42 and 48 is the smallest number among all common multiples of 42 and 48. The first few multiples of 42 and 48 are (42, 84, 126, 168, . . . ) and (48, 96, 144, 192, 240, 288, . . . ) respectively.
Also read: Least common multiple
What is LCM of 42 and 48?
The answer to this question is 336. The LCM of 42 and 48 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 42 and 48, is the smallest positive integer 336 which is divisible by both 42 and 48 with no remainder.
How to Find LCM of 42 and 48?
LCM of 42 and 48 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 42 and 48 Using Prime Factorisation Method
The prime factorisation of 42 and 48, respectively, is given by:
42 = (2 × 3 × 7) = 21 × 31 × 71 and
48 = (2 × 2 × 2 × 2 × 3) = 24 × 31
LCM (42, 48) = 336
LCM of 42 and 48 Using Division Method
We’ll divide the numbers (42, 48) by their prime factors to get the LCM of 42 and 48 using the division method (preferably common). The LCM of 42 and 48 is calculated by multiplying these divisors.
| 2 | 42 | 48 |
| 2 | 24 | 28 |
| 2 | 12 | 14 |
| 2 | 6 | 7 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (42, 48) = 336
LCM of 42 and 48 Using Listing the Multiples
To calculate the LCM of 42 and 48 by listing out the common multiples, list the multiples as shown below
| Multiples of 42 | Multiples of 48 |
| 42 | 48 |
| 84 | 96 |
| 126 | 144 |
| …. | …… |
| 336 | 336 |
The smallest common multiple of 42 and 48 is 336.
Therefore LCM (42, 48) = 336
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LCM of 42 and 48 Solved Example
Question: Find the smallest number that is divisible by 42 and 48 exactly.
Solution:
The smallest number that is divisible by 42 and 48 exactly is their LCM.
⇒ Multiples of 42 and 48:
Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, 336, . . . .
Multiples of 48 = 48, 96, 144, 192, 240, 288, 336, . . . .
Therefore, the LCM of 42 and 48 is 336.
Frequently Asked Questions on LCM of 42 and 48
What is the LCM of 42 and 48?
List the methods used to find the LCM of 42 and 48.
What is the Least Perfect Square Divisible by 42 and 48?
LCM of 42 and 48 = 2 × 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7] ⇒ Least perfect square divisible by each 42 and 48 = LCM(42, 48) × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84] Therefore, 7056 is the required number.
If the LCM of 48 and 42 is 336, Find its GCF.
Since the LCM of 48 and 42 = 336
⇒ 336 × GCF(48, 42) = 2016
Therefore, the GCF (greatest common factor) = 2016/336 = 6.
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