LCM of 15 and 45 is 45.The Least/Lowest Common multiple known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 15 and 45, 45 is the first(least or smallest) number that is common in the set of multiples of 15 and 45. The LCM is also known as LCD, Least Common Divisor. You can refer to the LCM for more details.
What is LCM of 15 and 45
The Least Common Multiple or Lowest Common Multiple of 15 and 45 is 45.
How to Find LCM of 15 and 45?
LCM of 15 and 45 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 45 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 15 and 45 can be expressed as;
15 = 3 × 5
45 = 3 × 3 × 5
Product of the union of prime factors of 15 and 45 will be the LCM
LCM (15, 45) = 3 × 3 × 5 = 45
LCM of 15 and 45 Using Division Method
In the Division Method, Follow the below steps
- Divide the numbers with the same prime factor starting from the smallest
- Increase the divisors gradually till the division becomes complete with remainders as one
- Product of prime divisors will be the LCM.
|
3 |
15 |
45 |
|
3 |
5 |
15 |
|
5 |
5 |
5 |
|
× |
1 |
1 |
Hence, LCM (15, 45) = 3 × 3 × 5 = 45
LCM of 15 and 45 Using Listing the Multiples
By listing all the multiples of the numbers 15 and 45, we can identify the least common multiple, which is the LCM. Below is the list of multiples for 15 and 45
|
Multiples of 15 |
Multiples of 45 |
|
15 |
45 |
|
30 |
90 |
|
45 |
135 |
LCM (15, 45) = 45
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 15 and 45?
Answer: 45 is the smallest number that is divisible by both 15 and 45.
What is the LCM for 5, 15 and 45?
Answer: LCM for 5, 15 and 45 is 45 as 5 is the prime multiple of 15 and 45.
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