LCM of 40 and 48 is 240. LCM of 40 and 48 is the smallest number among all common multiples of 40 and 48. The first few multiples of 40 and 48 are (40, 80, 120, 160, 200, 240, 280, . . . ) and (48, 96, 144, 192, 240, 288, . . . ) respectively. 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.
Also read: Least common multiple
What is LCM of 40 and 48?
The answer to this question is 240. The LCM of 40 and 48 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40 and 48, is the smallest positive integer 240 which is divisible by both 40 and 48 with no remainder.
How to Find LCM of 40 and 48?
LCM of 40 and 48 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40 and 48 Using Prime Factorisation Method
The prime factorisation of 40 and 48, respectively, is given by:
40 = (2 × 2 × 2 × 5) = 23 × 51 and
48 = (2 × 2 × 2 × 2 × 3) = 24 × 31
LCM (40, 48) = 240
LCM of 40 and 48 Using Division Method
We’ll divide the numbers (40, 48) by their prime factors to get the LCM of 40 and 48 using the division method (preferably common). The LCM of 40 and 48 is calculated by multiplying these divisors.
| 2 | 40 | 48 |
| 2 | 20 | 24 |
| 2 | 10 | 12 |
| 2 | 5 | 6 |
| 3 | 5 | 3 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (40, 48) = 240
LCM of 40 and 48 Using Listing the Multiples
To calculate the LCM of 40 and 48 by listing out the common multiples, list the multiples as shown below.
| Multiples of 40 | Multiples of 48 |
| 40 | 48 |
| 80 | 96 |
| 120 | 144 |
| 160 | 192 |
| 200 | 240 |
| 240 | 288 |
The smallest common multiple of 40 and 48 is 240.
Therefore LCM (40, 48) = 240
Related Articles
Video Lesson on Applications of LCM
LCM of 40 and 48 Solved Example
Question: The product of two numbers is 1920. If their GCD is 8, what is their LCM?
Solution:
Given: GCD = 8
Product of numbers = 1920
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1920/8
Therefore, the LCM is 240.
The probable combination for the given case is LCM(40, 48) = 240.
Frequently Asked Questions on LCM of 40 and 48
What is the LCM of 40 and 48?
List the methods used to find the LCM of 40 and 48.
What is the Relation Between GCF and LCM of 40, 48?
What is the Least Perfect Square Divisible by 40 and 48?
LCM of 40 and 48 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5] ⇒ Least perfect square divisible by each 40 and 48 = LCM(40, 48) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
If the LCM of 48 and 40 is 240, Find its GCF.
Since the LCM of 48 and 40 = 240
⇒ 240 × GCF(48, 40) = 1920
Therefore, the greatest common factor (GCF) = 1920/240 = 8.
Comments