LCM of 5, 6 and 9 is 90. The least common multiple denotes the smallest positive integer, which is multiple in a given set of numbers. Students can learn the LCM concept by referring to the article Least Common Multiple (LCM) formulated by experts. Practising the problems using this article improves logical approach and rational thinking abilities, which helps students solve the problems of the LCM concept with ease. Here, we will learn the simple way of finding the least common multiple of 5, 6 and 9 with a complete explanation.
What is LCM of 5, 6 and 9?
The Least Common Multiple of 5, 6 and 9 is 90.
How to Find LCM of 5, 6 and 9?
The LCM of 5, 6 and 9 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 5, 6 and 9 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 5, 6 and 9 can be expressed as;
5 = 5
6 = 2 × 3
9 = 3 × 3
LCM (5, 6, 9) = 2 × 3 × 3 × 5 = 90
LCM of 5, 6 and 9 Using Division Method
In the division method, we divide the numbers 5, 6 and 9 by a common prime number until the remainder is a prime number or one. The product of these divisors gives the least common multiple of 5, 6 and 9.
| 2 | 5 | 6 | 9 |
| 3 | 5 | 3 | 9 |
| 3 | 5 | 1 | 3 |
| 5 | 5 | 1 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (5, 6, 9) = 2 × 3 × 3 × 5 = 90
LCM of 5, 6 and 9 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The multiples of 5, 6 and 9 are as follows:
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ……….., 75, 80, 85, 90, ……..
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ……….., 72, 78, 84, 90, ……….
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …………
LCM (5, 6, 9) = 90
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 5, 6, 9 exactly?
Solution: The smallest number that is divisible by 5, 6, 9 exactly is their LCM. The LCM of 5, 6 and 9 is 90. Therefore, the smallest number that is divisible by 5, 6, 9 exactly is 90.
Frequently Asked Questions on LCM of 5, 6 and 9
What is the LCM of 5, 6 and 9?
Is the LCM of 5, 6 and 9 and the HCF of 5, 6, and 9 are same?
What are the methods used to find the LCM of 5, 6 and 9?
The following methods are used to find the LCM of 5, 6 and 9
Prime Factorisation
Division Method
Listing the Multiples
Find the least common multiple of 5, 6 and 9 using prime factorisation.
In this method, the given numbers are expressed as the product of prime factors to find the LCM
5 = 5
6 = 2 × 3
9 = 3 × 3
LCM (5, 6, 9) = 2 × 3 × 3 × 5 = 90
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