LCM of 9 and 30 is 90. The smallest number among all frequent multiples of 9 and 30 is the LCM. (9, 18, 27, 36, etc.) and (30, 60, 90, 120, 150, etc.) are the first few multiples of 9 and 30, respectively. There are three typical ways for calculating the LCM of 9 and 30: listing multiples, prime factorization, and division method. The LCM of any two integers is the value that is evenly divisible by the provided two numbers in mathematics.
Also read: Least common multiple
What is LCM of 9 and 30?
The answer to this question is 90. The LCM of 9 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 30, is the smallest positive integer 90 which is divisible by both 9 and 30 with no remainder.
How to Find LCM of 9 and 30?
LCM of 9 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 30 Using Prime Factorisation Method
The prime factorisation of 9 and 30, respectively, is given by:
9 = (3 × 3) = 32 and
30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (9, 30) = 90
LCM of 9 and 30 Using Division Method
We’ll divide the numbers (9, 30) by their prime factors to get the LCM of 9 and 30 using the division method (preferably common). The LCM of 9 and 30 is calculated by multiplying these divisors.
| 2 | 9 | 30 |
| 3 | 9 | 15 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 30) = 90
LCM of 9 and 30 Using Listing the Multiples
To calculate the LCM of 9 and 30 by listing out the common multiples, list the multiples as shown below
| Multiples of 9 | Multiples of 30 |
| 9 | 30 |
| 18 | 60 |
| 27 | 90 |
| ….. | 120 |
| 90 | 150 |
The smallest common multiple of 9 and 30 is 90.
Therefore LCM (9 30) = 90
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Video Lesson on Applications of LCM
LCM of 9 and 30 Solved Example
Find the smallest number that is divisible by 9 and 30 exactly.
Solution:
The smallest number that is divisible by 9 and 30 exactly is their LCM.
⇒ Multiples of 9 and 30:
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . .
Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, . . . .
Therefore, the LCM of 9 and 30 is 90.
Frequently Asked Questions on LCM of 9 and 30
What is the LCM of 9 and 30?
List the methods used to find the LCM of 9 and 30.
What is the Least Perfect Square Divisible by 9 and 30?
LCM of 9 and 30 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5] ⇒ Least perfect square divisible by each 9 and 30 = LCM(9, 30) × 2 × 5 = 900 [Square root of 900 = √900 = ±30] Therefore, 900 is the required number.
If the LCM of 30 and 9 is 90, Find its GCF.
Since the LCM of 30 and 9 = 90
⇒ 90 × GCF(30, 9) = 270
Therefore, the GCF = 270/90 = 3.
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