LCM of 45 and 63 is 315. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. For better learning of the concepts, students can refer to the article HCF and LCM developed by experts in simple language. The detailed explanation provided in this article helps students calculate the HCF and LCM of given numbers in an efficient manner. In this article, we will discuss how to find the least common multiple of 45 and 63.
What is LCM of 45 and 63?
The Least Common Multiple of 45 and 63 is 315.
How to Find LCM of 45 and 63?
We can obtain the LCM of 45 and 63 by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 45 and 63 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 45 and 63 can be denoted as;
45 = 3 × 3 × 5
63 = 3 × 3 × 7
LCM (45, 63) = 3 × 3 × 5 × 7 = 315
LCM of 45 and 63 Using Division Method
In the division method, we divide the numbers 45 and 63 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 45 and 63.
| 3 | 45 | 63 |
| 3 | 15 | 21 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Therefore, LCM (45, 63) = 3 × 3 × 5 × 7 = 315
LCM of 45 and 63 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the lowest common multiple among them. The below table represents the multiples of 45 and 63.
| Multiples of 45 | Multiples of 63 |
| 45 | 63 |
| 90 | 126 |
| 135 | 189 |
| 180 | 252 |
| 225 | 315 |
| 270 | 378 |
| 315 | 441 |
| 360 | 504 |
LCM (45, 63) = 315
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 45 and 63?
Solution: 315 is the smallest number that is divisible by both 45 and 63.
2. The GCD and LCM of the two numbers are 9 and 315. If one number is 63, calculate the other number.
Solution: Let the other number be p
We know that,
GCD × LCM = 63 × p
p = (GCD × LCM) / 63
p = (9 × 315) / 63
p = 45
Hence the other number is 45.
Frequently Asked Questions on LCM of 45 and 63
What is the LCM of 45 and 63?
What are the methods used to find the LCM of 45 and 63?
The following methods are used to find the LCM of 45 and 63:
Prime Factorisation
Division Method
Listing the Multiples
Which of the following is the highest common factor of 45 and 63? 10, 19, 11, 9
Find the GCF if the LCM of 45 and 63 is 315.
GCF × LCM = 45 × 63
Given
LCM = 315
GCF × 315 = 45 × 63
GCF = 9
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