LCM of 90 and 105 is 630. The least common multiple of 90 and 105 can be obtained by prime factorisations, division method and list of multiples. Least Common Multiple (LCM) is well structured by experts in a simple and lucid manner so that students understand the concept thoroughly. Students can make use of this article to grasp the LCM concept more effectively. Learn the simple method of calculating the least common multiple of 90 and 105 with solved examples and FAQs here.
What is LCM of 90 and 105?
The Least Common Multiple of 90 and 105 is 630.
How to Find LCM of 90 and 105?
LCM of 90 and 105 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 90 and 105 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree.
90 = 2 × 3 × 3 × 5
105 = 3 × 5 × 7
LCM (90, 105) = 2 × 3 × 3 × 5 × 7 = 630
LCM of 90 and 105 Using Division Method
In the division method, to determine the least common multiple of 90 and 105, we divide the numbers 90 and 105 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 90 and 105.
| 2 | 90 | 105 |
| 3 | 45 | 105 |
| 3 | 15 | 35 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (90, 105) = 2 × 3 × 3 × 5 × 7 = 630
LCM of 90 and 105 Using Listing the Multiples
In this method, we list the multiples of 90 and 105 to find the least common multiple among them. Let us glance at the multiples of 90 and 105 from the table given below.
| Multiples of 90 | Multiples of 105 |
| 90 | 105 |
| 180 | 210 |
| 270 | 315 |
| 360 | 420 |
| 450 | 525 |
| 540 | 630 |
| 630 | 735 |
LCM (90, 105) = 630
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 90 and 105?
Solution: 630 is the smallest number that is divisible by both 90 and 105.
2. The product of two numbers is 9450. Find the LCM if their GCD is 15.
Solution: Given
GCD = 15
Product of numbers = 9450
LCM × GCD = Product of numbers
LCM = Product of numbers / GCD
LCM = 9450 / 15
LCM = 630
Frequently Asked Questions on LCM of 90 and 105
What is the LCM of 90 and 105?
Is the LCM of 90 and 105 the same as the HCF of 90 and 105?
Name the methods used to find the least common multiple of 90 and 105.
The methods used to find the least common multiple of 90 105 are:
Prime Factorisation
Division method
Listing the Multiples
What is the GCF if the LCM of 90 and 105 is 630?
GCF × LCM = 90 × 105
Given
LCM = 630
GCF × 630 = 90 × 105
GCF = 15
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