LCM of 30 and 22 is 330. 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 22 and 30 is the smallest number among all common multiples of 22 and 30. The first few multiples of 22 and 30 are (22, 44, 66, 88, 110, 132, . . . ) and (30, 60, 90, 120, 150, . . . ) respectively.
Also read: Least common multiple
What is LCM of 30 and 22?
The answer to this question is 330. The LCM of 30 and 22 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 30 and 22, is the smallest positive integer 330 which is divisible by both 30 and 22 with no remainder.
How to Find LCM of 30 and 22?
LCM of 30 and 22 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 22 Using Prime Factorisation Method
The prime factorisation of 30 and 22, respectively, is given by:
22 = (2 × 11) = 21 × 111 and
30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (30, 22) = 330
LCM of 30 and 22 Using Division Method
We’ll divide the numbers (30, 22) by their prime factors to get the LCM of 30 and 22 using the division method (preferably common). The LCM of 30 and 22 is calculated by multiplying these divisors.
| 2 | 30 | 22 |
| 3 | 15 | 11 |
| 5 | 5 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (30, 22) = 330
LCM of 30 and 22 Using Listing the Multiples
To calculate the LCM of 30 and 22 by listing out the common multiples, list the multiples as shown below
| Multiples of 30 | Multiples of 22 |
| 30 | 22 |
| 60 | 44 |
| 90 | 66 |
| 120 | 88 |
| …… | …… |
| 330 | 330 |
The smallest common multiple of 30 and 22 is 330.
Therefore LCM (30, 22) = 330
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LCM of 30 and 22 Solved Example
Verify the relationship between GCF and LCM of 22 and 30.
Solution:
The relation between GCF and LCM of 22 and 30 is given as,
LCM(22, 30) × GCF(22, 30) = Product of 22, 30
Prime factorization of 22 and 30 is given as, 22 = (2 × 11)
= 2 × 11 and
30 = (2 × 3 × 5) = 2 × 3 × 5
LCM(22, 30) = 330
GCF(22, 30) = 2
LHS = LCM(22, 30) × GCF(22, 30) = 330 × 2 = 660
RHS = Product of 22, 30 = 22 × 30 = 660
⇒ LHS = RHS = 660
Hence, verified.
Frequently Asked Questions on LCM of 30 and 22
What is the LCM of 30 and 22?
List the methods used to find the LCM of 30 and 22.
What is the Relation Between GCF and LCM of 22, 30?
Which of the following is the LCM of 22 and 30? 330, 16, 3, 24
What is the Least Perfect Square Divisible by 22 and 30?
LCM of 22 and 30 = 2 × 3 × 5 × 11 [Incomplete pair(s): 2, 3, 5, 11] ⇒ Least perfect square divisible by each 22 and 30 = LCM(22, 30) × 2 × 3 × 5 × 11 = 108900 [Square root of 108900 = √108900 = ±330] Therefore, 108900 is the required number.
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