LCM of 45 and 90 is 90. LCM depicts the least common factor or multiple of any two or more given numbers. LCM with Examples is prepared by experts who have a vast experience in the teaching field. The clear explanation of the concepts in this article enhances learning process of students and helps them to score high marks in exams. Let us grasp the simple process of calculating the least common multiple of 45 and 90 with suitable examples and FAQs in this article.
What is LCM of 45 and 90?
The Least Common Multiple of 45 and 90 is 90.
How to Find LCM of 45 and 90?
LCM of 45 and 90 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 45 and 90 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 45 and 90 are expressed as;
45 = 3 × 3 × 5
90 = 2 × 3 × 3 × 5
LCM (45, 90) = 2 × 3 × 3 × 5 = 90
LCM of 45 and 90 Using Division Method
In the division method, to find the least common multiple of 45 and 90, we divide the numbers 45 and 90 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 45 and 90.
| 2 | 45 | 90 |
| 3 | 45 | 45 |
| 3 | 15 | 15 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (45, 90) = 2 × 3 × 3 × 5 = 90
LCM of 45 and 90 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. Let us have a look at the multiples of 45 and 90 from the table given below.
| Multiples of 45 | Multiples of 90 |
| 45 | 90 |
| 90 | 180 |
| 135 | 270 |
| 180 | 360 |
| 225 | 450 |
LCM (45, 90) = 90
Related Articles
- Lowest Common Multiple (LCM)
- Prime Factorisation and Division Method for LCM and HCF
- LCM of Two Numbers
- LCM calculator
- LCM Formula
- HCF and LCM
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 45 and 90?
Solution: 90 is the smallest number that is divisible by both 45 and 90.
2. What is the greatest common factor of 45 and 90?
Solution: 45 is the greatest common factor of 45 and 90.
Frequently Asked Questions on LCM of 45 and 90
What is the LCM of 45 and 90?
What is the LCM of 45 and 90 and the HCF of 45 and 90?
70 is the LCM of 45 and 90. True or False.
Name the methods used to find the LCM of 45 and 90.
The following methods are used to find the LCM of 45 and 90
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 45 and 90 is 90?
GCF × LCM = 45 × 90
Given
LCM = 90
GCF × 90 = 45 × 90
GCF = 45
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