LCM of 30 and 45 is 90. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. Between all common multiples of 30 and 45, the LCM of 30 and 45 is the smallest number. (30, 60, 90, 120, 150, etc.) and (45, 90, 135, 180, etc.) are the first few multiples of 30 and 45. To find the LCM of 30 and 45, you can use one of three methods: listing multiples, prime factorization, or division.
Also read: Least common multiple
What is LCM of 30 and 45?
The answer to this question is 90. The LCM of 30 and 45 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 30 and 45, is the smallest positive integer 90 which is divisible by both 30 and 45 with no remainder.
How to Find LCM of 30 and 45?
LCM of 30 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 45 Using Prime Factorisation Method
The prime factorisation of 30 and 45, respectively, is given by:
30 = (2 × 3 × 5) = 21 × 31 × 51 and
45 = (3 × 3 × 5) = 32 × 51
LCM (30, 45) = 90
LCM of 30 and 45 Using Division Method
We’ll divide the numbers (30, 45) by their prime factors to get the LCM of 30 and 45 using the division method (preferably common). The LCM of 30 and 45 is calculated by multiplying these divisors.
|
2 |
30 |
45 |
|
3 |
15 |
45 |
|
3 |
5 |
15 |
|
5 |
5 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (30, 45) = 90
LCM of 30 and 45 Using Listing the Multiples
To calculate the LCM of 30 and 45 by listing out the common multiples, list the multiples as shown below:
|
Multiples of 30 |
Multiples of 45 |
|
30 |
45 |
|
60 |
90 |
|
90 |
135 |
|
120 |
180 |
|
150 |
225 |
The smallest common multiple of 30 and 45 is 90.
LCM (30, 45) = 90
Related Articles
Video Lesson on Applications of LCM
LCM of 30 and 45 Solved Example
The product of two numbers is 1350. If their GCD is 15, what is their LCM?
Given: GCD = 15
product of numbers = 1350
LCM × GCD = product of numbers
LCM = Product/GCD = 1350/15
Therefore, the LCM is 90.
The probable combination for the given case is LCM(30, 45) = 90.
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