LCM of 63 and 105 is 315. LCM depicts the least common factor or multiple of any two or more given numbers. LCM with Examples is the perfect study guide for students who are facing trouble in finding the least common multiple of given numbers. This article is well-structured by high professional teachers who have years of experience. Here, we will discuss how to verify the least common multiple of 63 and 105 with the help of solved examples and FAQs.
What is LCM of 63 and 105?
The Least Common Multiple of 63 and 105 is 315.
How to Find LCM of 63 and 105?
LCM of 63 and 105 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 63 and 105 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 63 and 105 are expressed as;
63 = 3 × 3 × 7
105 = 3 × 5 × 7
LCM (63, 105) = 3 × 3 × 5 × 7 = 315
LCM of 63 and 105 Using Division Method
In the division method, to find the least common multiple of 63 and 105, we divide the numbers 63 and 105 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 63 and 105.
| 3 | 63 | 105 |
| 3 | 21 | 35 |
| 5 | 7 | 35 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (63, 105) = 3 × 3 × 5 × 7 = 315
LCM of 63 and 105 Using Listing the Multiples
In this method, we list down the multiples of given numbers to calculate the lowest common multiple among them. Let us have a look at the multiples of 63 and 105 from the table given below.
| Multiples of 63 | Multiples of 105 |
| 63 | 105 |
| 126 | 210 |
| 189 | 315 |
| 252 | 420 |
| 315 | 525 |
| 378 | 630 |
LCM (63, 105) = 315
Related Articles
Prime Factorisation 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 63 and 105?
Solution: 315 is the smallest number that is divisible by both 63 and 105.
2. What is the lowest common factor of 63 and 105?
Solution: The lowest common factor of 63 and 105 is 315.
Frequently Asked Questions on LCM of 63 and 105
What is the LCM of 63 and 105?
Is the LCM of 63 and 105 the same as the HCF of 63 and 105?
515 is the LCM of 63 and 105. True or False.
What are the methods used to find the LCM of 63 and 105?
The methods used to find the LCM of 63 and 105 are
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 63 and 105 is 315?
GCF × LCM = 63 × 105
Given
LCM = 315
GCF × 315 = 63 × 105
GCF = 21
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