LCM of 8 and 48 is 48. The smallest number among all common multiples of 8 and 48 is the LCM of 8 and 48. (8, 16, 24, 32, 40, 48, 56, etc.) and (48, 96, 144, 192, 240, 288, etc.) are the first few multiples of 8 and 48, respectively. To find the LCM of 8 and 48, there are three main methods: prime factorization, listing multiples, and division. 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 8 and 48?
The answer to this question is 48. The LCM of 8 and 48 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8 and 48, is the smallest positive integer 48 which is divisible by both 8 and 48 with no remainder.
How to Find LCM of 8 and 48?
LCM of 8 and 48 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 48 Using Prime Factorisation Method
The prime factorisation of 8 and 48, respectively, is given by:
8 = (2 × 2 × 2) = 23 and
48 = (2 × 2 × 2 × 2 × 3) = 24 × 31
LCM (8, 48) = 48
LCM of 8 and 48 Using Division Method
We’ll divide the numbers (8, 48) by their prime factors to get the LCM of 8 and 48 using the division method (preferably common). The LCM of 8 and 48 is calculated by multiplying these divisors.
| 2 | 8 | 48 |
| 2 | 4 | 24 |
| 2 | 2 | 12 |
| 2 | 1 | 6 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (8, 48) = 48
LCM of 8 and 48 Using Listing the Multiples
To calculate the LCM of 8 and 48 by listing out the common multiples, list the multiples as shown below
| Multiples of 8 | Multiples of 48 |
| 8 | 48 |
| 16 | 96 |
| 24 | 144 |
| 32 | 192 |
| 40 | 240 |
| 48 | 288 |
The smallest common multiple of 8 and 48 is 48.
Therefore LCM (8, 48) = 48
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LCM of 8 and 48 Solved Example
The GCD and LCM of two numbers are 8 and 48 respectively. If one number is 8, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 8 × p
⇒ p = (GCD × LCM)/8
⇒ p = (8 × 48)/8
⇒ p = 48
Therefore, the other number is 48.
Frequently Asked Questions on LCM of 8 and 48
What is the LCM of 8 and 48?
List the methods used to find the LCM of 8 and 48.
What is the Least Perfect Square Divisible by 8 and 48?
LCM of 8 and 48 = 2 × 2 × 2 × 2 × 3 [Incomplete pair(s): 3] ⇒ Least perfect square divisible by each 8 and 48 = LCM(8, 48) × 3 = 144 [Square root of 144 = √144 = ±12] Therefore, 144 is the required number.
If the LCM of 48 and 8 is 48, Find its GCF.
Since the LCM of 48 and 8 = 48
⇒ 48 × GCF(48, 8) = 384
Therefore, the GCF (greatest common factor) = 384/48 = 8.
How to Find the LCM of 8 and 48 by Prime Factorization?
⇒ LCM of 8, 48 = 24 × 31 = 48.
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