LCM of 12 and 90 is 180. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. The smallest number among all common multiples of 12 and 90 is the LCM of 12 and 90. (12, 24, 36, 48, 60, etc.) and (90, 180, 270, 360, 450, etc.) are the first few multiples of 12 and 90, respectively.
Also read: Least common multiple
What is LCM of 12 and 90?
The answer to this question is 180. The LCM of 12 and 90 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 90, is the smallest positive integer 180 which is divisible by both 12 and 90 with no remainder.
How to Find LCM of 12 and 90?
LCM of 12 and 90 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 90 Using Prime Factorisation Method
The prime factorisation of 12 and 90, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31 and
90 = (2 × 3 × 3 × 5) = 21 × 32 × 51
LCM (12, 90) = 180
LCM of 12 and 90 Using Division Method
We’ll divide the numbers (12, 90) by their prime factors to get the LCM of 12 and 90 using the division method (preferably common). The LCM of 12 and 90 is calculated by multiplying these divisors.
| 2 | 12 | 90 |
| 2 | 6 | 45 |
| 3 | 3 | 45 |
| 3 | 1 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 90) = 180
LCM of 12 and 90 Using Listing the Multiples
To calculate the LCM of 12 and 90 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 90 |
| 12 | 90 |
| 24 | 180 |
| 36 | 270 |
| …… | 360 |
| 180 | 450 |
The smallest common multiple of 12 and 90 is 180.
Therefore LCM (12, 90) = 180
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LCM of 12 and 90 Solved Example
The product of two numbers is 1080. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 1080
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1080/6
Therefore, the LCM is 180.
The probable combination for the given case is LCM(12, 90) = 180.
Frequently Asked Questions on LCM of 12 and 90
What is the LCM of 12 and 90?
List the methods used to find the LCM of 12 and 90.
If the LCM of 90 and 12 is 180, Find its GCF.
Since the LCM of 90 and 12 = 180
⇒ 180 × GCF(90, 12) = 1080
Therefore, the greatest common factor = 1080/180 = 6.
What is the Least Perfect Square Divisible by 12 and 90?
LCM of 12 and 90 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5] ⇒ Least perfect square divisible by each 12 and 90 = LCM(12, 90) × 5 = 900 [Square root of 900 = √900 = ±30] Therefore, 900 is the required number.
How to Find the LCM of 12 and 90 by Prime Factorization?
⇒ LCM of 12, 90 = 22 × 32 × 5 = 180.
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