LCM of 15 and 40 is 120. The smallest number among all frequent multiples of 15 and 40 is the LCM of 15 and 40. (15, 30, 45, 60, 75, 90, 105, etc.) and (40, 80, 120, 160, etc.) are the first few multiples of 15 and 40, respectively. To find the LCM of 15 and 40, there are three main methods: division, prime factorization, and listing multiples. In mathematics, the LCM of any two numbers is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 15 and 40?
The answer to this question is 120. The LCM of 15 and 40 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 15 and 40, is the smallest positive integer 120 which is divisible by both 15 and 40 with no remainder.
How to Find LCM of 15 and 40?
LCM of 15 and 40 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 40 Using Prime Factorisation Method
The prime factorisation of 15 and 40, respectively, is given by:
15 = (3 × 5) = 31 × 51
40 = (2 × 2 × 2 × 5) = 23 × 51
LCM (15, 40) = 120
LCM of 15 and 40 Using Division Method
We’ll divide the numbers (15, 40) by their prime factors to get the LCM of 15 and 40 using the division method (preferably common). The LCM of 15 and 40 is calculated by multiplying these divisors.
| 2 | 15 | 40 |
| 2 | 15 | 20 |
| 2 | 15 | 10 |
| 3 | 15 | 5 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (15, 40) = 120
LCM of 15 and 40 Using Listing the Multiples
To calculate the LCM of 15 and 40 by listing out the common multiples, list the multiples as shown below
| Multiples of 15 | Multiples of 40 |
| 15 | 40 |
| 30 | 80 |
| 45 | 120 |
| 60 | 160 |
| 75 | 200 |
| 90 | 240 |
| 105 | 280 |
| 120 | 320 |
The smallest common multiple of 15 and 40 is 120.
LCM (15, 40) = 120
Related Articles
Video Lesson on Applications of LCM
LCM of 15 and 40 Solved Example
Question: The product of two numbers is 600. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
product of numbers = 600
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 600/5
Therefore, the LCM is 120.
The probable combination for the given case is LCM(15, 40) = 120.
Comments