LCM of 30 and 90 is 90. 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. LCM of 30 and 90 is the smallest number among all common multiples of 30 and 90. The first few multiples of 30 and 90 are (30, 60, 90, 120, 150, 180, 210, . . . ) and (90, 180, 270, 360, 450, 540, 630, . . . ) respectively.
Also read: Least common multiple
What is LCM of 30 and 90?
The answer to this question is 90. The LCM of 30 and 90 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 30 and 90, is the smallest positive integer 90 which is divisible by both 30 and 90 with no remainder.
How to Find LCM of 30 and 90?
LCM of 30 and 90 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 90 Using Prime Factorisation Method
The prime factorisation of 30 and 90, respectively, is given by:
30 = (2 × 3 × 5) = 21 × 31 × 51 and
90 = (2 × 3 × 3 × 5) = 21 × 32 × 51
LCM (30, 90) = 90
LCM of 30 and 90 Using Division Method
We’ll divide the numbers (30, 90) by their prime factors to get the LCM of 30 and 90 using the division method (preferably common). The LCM of 30 and 90 is calculated by multiplying these divisors.
| 2 | 30 | 90 |
| 3 | 15 | 45 |
| 3 | 5 | 15 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (30, 90) = 90
LCM of 30 and 90 Using Listing the Multiples
To calculate the LCM of 30 and 90 by listing out the common multiples, list the multiples as shown below
| Multiples of 30 | Multiples of 90 |
| 30 | 90 |
| 60 | 180 |
| 90 | 270 |
| 120 | 360 |
| 150 | 450 |
The smallest common multiple of 30 and 90 is 90.
Therefore LCM (30, 90) = 90
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LCM of 30 and 90 Solved Example
The GCD and LCM of two numbers are 30 and 90 respectively. If one number is 30, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 30 × a
⇒ a = (GCD × LCM)/30
⇒ a = (30 × 90)/30
⇒ a = 90
Therefore, the other number is 90.
Frequently Asked Questions on LCM of 30 and 90
What is the LCM of 30 and 90?
List the methods used to find the LCM of 30 and 90.
What is the Relation Between GCF and LCM of 30, 90?
If the LCM of 90 and 30 is 90, Find its GCF.
Since the LCM of 90 and 30 = 90
⇒ 90 × GCF(90, 30) = 2700
Therefore, the GCF = 2700/90 = 30.
How to Find the LCM of 30 and 90 by Prime Factorization?
⇒ LCM of 30, 90 = 90.
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