LCM of 9 and 11 is 99. In mathematics, the LCM of any two numbers is the value that is evenly divisible by the two values. The smallest number among all common multiples of 9 and 11 is the LCM of 9 and 11. (9, 18, 27, 36, 45, 54, etc.) and (11, 22, 33, 44, 55, etc.) are the first few multiples of 9 and 11. To find the LCM of 9 and 11, you can use one of three methods: prime factorization, division, or listing multiples.
What is LCM of 9 and 11?
The answer to this question is 99. The LCM of 9 and 11 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 11, is the smallest positive integer 99 which is divisible by both 9 and 11 with no remainder.
Also read: Least common multiple
How to Find LCM of 9 and 11?
LCM of 9 and 11 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 11 Using Prime Factorisation Method
The prime factorisation of 9 and 11, respectively, is given by:
9 = (3 × 3) = 32 and
(11) = 111
LCM (9, 12) = 36
LCM of 9 and 11 Using Division Method
We’ll divide the numbers (9, 11) by their prime factors to get the LCM of 9 and 11 using the division method (preferably common). The LCM of 9 and 11 is calculated by multiplying these divisors.
| 3 | 9 | 11 |
| 3 | 3 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 11) = 99
LCM of 9 and 11 Using Listing the Multiples
To calculate the LCM of 9 and 11 by listing out the common multiples, list the multiples as shown below
| Multiples of 9 | Multiples of 11 |
| 9 | 11 |
| 18 | 22 |
| 27 | 33 |
| 36 | 44 |
| 45 | 55 |
| 54 | 66 |
| 63 | 77 |
| 72 | 88 |
| 81 | 99 |
| 90 | 121 |
| 99 | 132 |
The smallest common multiple of 9 and 11 is 99.
LCM (9, 11) = 99
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LCM of 9 and 11 Solved Example
Question: Verify the relationship between GCF and LCM of 9 and 11.
Solution: The relation between GCF and LCM of 9 and 11 is given as,
LCM(9, 11) × GCF(9, 11) = Product of 9, 11
Prime factorization of 9 and 11 is given as, 9 = (3 × 3) = 32 and 11 = (11) = 111
LCM(9, 11) = 99
GCF(9, 11) = 1
LHS = LCM(9, 11) × GCF(9, 11) = 99 × 1 = 99
RHS = Product of 9, 11 = 9 × 11 = 99
LHS = RHS = 99
Hence, verified.
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