LCM of 15, 30 and 90 is 90. LCM is the method to find the smallest possible multiple of two or more numbers. The team of subject experts prepared the article LCM of Two Numbers with the aim to boost the student’s confidence level and also help them to work on their weak points. This article explains the concept in a well-structured format so that student’s clear their doubts immediately. In this article, let us have a look at how to calculate the least common multiple of 15, 30 and 90 with simple steps.
What is LCM of 15, 30 and 90?
The Least Common Multiple of 15, 30 and 90 is 90.
How to Find LCM of 15, 30 and 90?
LCM of 15, 30 and 90 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 15, 30 and 90 Using Prime Factorisation Method
Here, 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. Hence, the numbers 15, 30 and 90 can be expressed as;
15 = 3 × 5
30 = 2 × 3 × 5
90 = 2 × 3 × 3 × 5
LCM (15, 30, 90) = 2 × 3 × 3 × 5 = 90
LCM of 15, 30 and 90 Using Division Method
In the division method, to find the least common multiple of 15, 30 and 90, we divide the numbers 15, 30 and 90 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 15, 30 and 90.
| 2 | 15 | 30 | 90 |
| 3 | 15 | 15 | 45 |
| 3 | 5 | 5 | 15 |
| 5 | 5 | 5 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (15, 30, 90) = 2 × 3 × 3 × 5 = 90
LCM of 15, 30 and 90 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. Check the multiples of 15, 30 and 90 mentioned below.
| Multiples of 15 | Multiples of 30 | Multiples of 90 |
| 15 | 30 | 90 |
| 30 | 60 | 180 |
| 45 | 90 | 270 |
| 60 | 120 | 360 |
| 75 | 150 | 450 |
| 90 | 180 | 540 |
| 105 | 210 | 630 |
LCM (15, 30, 90) = 90
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 15, 30, 90 exactly?
Solution: The LCM of 15, 30 and 90 will be the smallest number that is divisible by 15, 30, 90 exactly. We know that 90 is the LCM of 15, 30 and 90. Therefore the smallest number that is divisible by 15, 30, 90 exactly is 90.
2. Which of the following is the least common multiple of 15, 30 and 90?
90, 85, 120, 300
Solution: The smallest number that is divisible by 15, 30, 90 exactly is the lowest common multiple of 15, 30 and 90. The number which satisfies this condition is 90.
Frequently Asked Questions on LCM of 15, 30 and 90
What is the LCM of 15, 30 and 90?
What is the difference between the LCM of 15, 30 and 90 and the HCF of 15, 30 and 90?
Is 80 the LCM of 15, 30 and 90?
Mention the methods used to determine the LCM of 15, 30 and 90.
The following methods are used to determine the LCM of 15, 30 and 90
Prime Factorisation
Division Method
Listing the Multiples
Determine the LCM of 15, 30 and 90 using the prime factorisation method.
Here, to find the LCM, we write the numbers as the product of prime factors
15 = 3 × 5
30 = 2 × 3 × 5
90 = 2 × 3 × 3 × 5
LCM (15, 30, 90) = 2 × 3 × 3 × 5 = 90
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