LCM of 10 and 45 is 90. In mathematics, the LCM of any two numbers is the value that is evenly divisible by the two values. The smallest number among all common multiples of 10 and 45 is the LCM of 10 and 45. (10, 20, 30, 40, 50, 60, etc.) and (45, 90, 135, 180, 225, etc.) are the first few multiples of 10 and 45, respectively. To find the LCM of 10 and 45, there are three main methods: prime factorization, listing multiples, and division.
Also read: Least common multiple
What is LCM of 10 and 45?
The answer to this question is 90. The LCM of 10 and 45 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 45, is the smallest positive integer 90 which is divisible by both 10 and 45 with no remainder.
How to Find LCM of 10 and 45?
LCM of 10 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 45 Using Prime Factorisation Method
The prime factorisation of 10 and 45, respectively, is given by:
10 = (2 × 5) = 21 × 51 and
45 = (3 × 3 × 5) = 32 × 51
LCM (10, 45) = 90
LCM of 10 and 45 Using Division Method
We’ll divide the numbers (10, 45) by their prime factors to get the LCM of 10 and 45 using the division method (preferably common). The LCM of 10 and 45 is calculated by multiplying these divisors.
| 2 | 10 | 45 |
| 3 | 5 | 45 |
| 3 | 5 | 15 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (10, 45) = 90
LCM of 10 and 45 Using Listing the Multiples
To calculate the LCM of 10 and 45 by listing out the common multiples, list the multiples as shown below.
| Multiples of 10 | Multiples of 45 |
| 10 | 45 |
| 20 | 90 |
| 30 | 135 |
| 40 | 180 |
| 50 | 225 |
| 60 | 270 |
| 70 | – |
| 80 | – |
| 90 | – |
The smallest common multiple of 10 and 45 is 90.
LCM (10, 45) = 90
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Video Lesson on Applications of LCM
LCM of 10 and 45 Solved Example
Question: The product of two numbers is 450. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
product of numbers = 450
LCM × GCD = product of numbers
LCM = Product/GCD = 450/5
Therefore, the LCM is 90.
The probable combination for the given case is LCM(10, 45) = 90.
Frequently Asked Questions on LCM of 10 and 45
What is the Relation Between GCF and LCM of 10, 45?
What are the Methods to Find LCM of 10 and 45?
Listing Multiples
Division Method
Prime Factorization Method
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