LCM of 8, 9 and 10 is 360. LCM denotes the smallest positive number that is a multiple of two or more numbers. The article Least Common Multiple (LCM) provides a good hold on the LCM concept, which is essential to score excellent marks in exams. The simple technique to find the LCM of given numbers can be learnt by following this article on a daily basis. Let us learn how to find the least common multiple of 8, 9 and 10 with the help of solved examples and FAQs here.
What is LCM of 8, 9 and 10?
The Least Common Multiple of 8, 9 and 10 is 360.
How to Find LCM of 8, 9 and 10?
LCM of 8, 9 and 10 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 8, 9 and 10 Using Prime Factorisation Method
In the prime factorisation method, LCM of 8, 9 and 10 can be obtained by multiplying prime factors raised to their respective highest power.
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
LCM (8, 9, 10) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 8, 9 and 10 Using Division Method
In the division method, to find the LCM, we divide the numbers 8, 9 and 10 by their prime factors until we get the result as one in the complete row. The product of these divisors indicates the least common multiple of 8, 9 and 10.
| 2 | 8 | 9 | 10 |
| 2 | 4 | 9 | 5 |
| 2 | 2 | 9 | 5 |
| 3 | 1 | 9 | 5 |
| 3 | 1 | 3 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (8, 9, 10) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 8, 9 and 10 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the least common multiple among them. The multiples of 8, 9 and 10 are provided below.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ………, 328, 336, 344, 352, 360,……..
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ……,324, 333, 342, 351, 360,……..
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ……,320, 330, 340, 350, 360,…..
LCM (8, 9, 10) = 360
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 8, 9, 10 exactly?
Solution: The smallest number that is divisible by 8, 9, 10 exactly is their LCM. Here the LCM of 8, 9 and 10 is 360. Therefore the smallest number that is divisible by 8, 9, 10 exactly is 360.
Frequently Asked Questions on LCM of 8, 9 and 10
What is the LCM of 8, 9 and 10?
Is the LCM of 8, 9 and 10 the same as the HCF of 8, 9 and 10?
Mention the methods used to find the least common multiple of 8, 9 and 10.
The following methods are used to find the least common multiple of 8, 9 and 10:
Prime Factorisation
Division method
Listing the Multiples
How to find the LCM of 8, 9 and 10 using the prime factorisation method?
To find the LCM using prime factorisation, we express the numbers as the product of prime factors
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
LCM (8, 9, 10) = 2 × 2 × 2 × 3 × 3 × 5 = 360
Which of the following is the LCM of 8, 9 and 10? 200, 260, 100, 360.
The smallest common multiple of 8, 9 and 10 is their LCM value. The number which satisfies this condition is 360.
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