LCM of 9 and 10 is 90. In mathematics, the LCM of any two numbers is the value that is evenly divisible by the two values. To find the LCM of Two Numbers that is 9 and 12, you can use one of three methods: division, listing multiples, or prime factorization. The smallest number among all common multiples of 9 and 10 is the LCM of 9 and 10. (9, 18, 27, 36, 45, 54, 63, etc.) and (10, 20, 30, 40, etc.) are the first few multiples of 9 and 10.
What is LCM of 9 and 10?
The answer to this question is 90. The LCM of 9 and 10 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 10, is the smallest positive integer 90 which is divisible by both 9 and 10 with no remainder.
Also read: Least common multiple
How to Find LCM of 9 and 10?
LCM of 9 and 10 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 10 Using Prime Factorisation Method
The prime factorisation of 9 and 10, respectively, is given by:
9 = 3 x 3 = 3²
10 = (2 × 5) = 21 × 51
LCM (9, 10) = 90
LCM of 9 and 10 Using Division Method
We’ll divide the numbers (9, 10) by their prime factors to get the LCM of 9 and 10 using the division method (preferably common). The LCM of 9 and 10 is calculated by multiplying these divisors.
| 2 | 9 | 10 |
| 3 | 9 | 5 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 10) = 90
LCM of 9 and 10 Using Listing the Multiples
To calculate the LCM of 9 and 10 by listing out the common multiples, list the multiples as shown below.
| Multiples of 9 | Multiples of 10 |
| 9 | 10 |
| 18 | 20 |
| 27 | 30 |
| 36 | 40 |
| 45 | 50 |
| 54 | 60 |
| 63 | 70 |
| 72 | 80 |
| 81 | 90 |
| 90 | 100 |
The smallest common multiple of 9 and 10 is 90.
LCM (9, 10) = 90
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LCM of 9 and 10 Solved Example
The product of two numbers is 90. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 90
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 90/1
Therefore, the LCM is 90.
The probable combination for the given case is LCM(9, 10) = 90.
Frequently Asked Questions on LCM of 9 and 10
What is the LCM of 9 and 10?
List the methods used to find the LCM of 9 and 10.
Find the smallest number that is divisible by 9 and 10 exactly.
⇒ Multiples of 9 and 10:
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . .
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, . . . .
Therefore, the LCM of 9 and 10 is 90..
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