LCM of 15 and 28 is 420.The Least Common Multiple or Lowest Common Multiple known as LCM is the smallest number that is divisible by the given numbers. In the given set of numbers 15 and 28, 420 is the first(least or smallest) number that is common in the set of multiples of 15 and 28. The LCM is also known as LCD, Least Common Divisor. You can refer to LCM for all details.
What is LCM of 15 and 28
The Least Common Multiple or Lowest Common Multiple of 15 and 28 is 420.
How to Find LCM of 15 and 28?
LCM of 15 and 28 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 28 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 15 and 28 can be expressed as;
15 = 3 × 5
28 = 2 × 2 × 7
Since there are no common prime factors, the product of all the prime factors is the LCM.
LCM (15, 28) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 15 and 28 Using Division Method
In the Division Method, the given numbers 15 and 28 are divided together. Since there are no common prime divisors, the product of all the common prime factors of 15 and 28 is the LCM.
|
2 |
15 |
28 |
|
2 |
15 |
14 |
|
3 |
15 |
7 |
|
5 |
5 |
7 |
|
7 |
1 |
7 |
|
× |
1 |
1 |
Hence, LCM (15, 28) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 15 and 28 Using Listing the Multiples
By listing all the multiples of 15 and 28, we can identify the LCM. Below is the list of multiples for 15 and 28
Multiples of 15
15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450
Multiples of 28
28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476
LCM (15, 28) = 420
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 15 and 28?
Answer: 420 is the smallest number that is divisible by both 15 and 28.
What is the LCM for 5, 15 and 28?
Answer: LCM for 5, 15 and 28 is 420 as 5 is the prime factor of 15.
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