LCM of 16 and 30 is 240. The common multiple divisible by 16 and 30 helps you calculate the LCM value. The least common multiple of 16 and 30 can be found by having a good knowledge of the multiplication operation which is crucial in Maths. (16, 32, 48, 64, 80, 96, 112, ….) and (30, 60, 90, 120, 150, 180, 210,….) are the first few multiples of 16 and 30. Few methods such as division, prime factorisation and listing of multiples can be used to determine the LCM value.
Also read: Least common multiple
What is LCM of 16 and 30?
The answer to this question is 240. The LCM of 16 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 16 and 30, is the smallest positive integer 240 which is divisible by both 16 and 30 with no remainder.
How to Find LCM of 16 and 30?
LCM of 16 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 16 and 30 Using Prime Factorisation Method
The prime factorisation of 16 and 30, respectively, is given by:
16 = 2 x 2 x 2 x 2 = 2⁴
30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
LCM (16, 30) = 240
LCM of 16 and 30 Using Division Method
We’ll divide the numbers (16, 30) by their prime factors to get the LCM of 16 and 30 using the division method (preferably common). The LCM of 16 and 30 is calculated by multiplying these divisors.
|
2 |
16 |
30 |
|
2 |
8 |
15 |
|
2 |
4 |
15 |
|
2 |
2 |
15 |
|
3 |
1 |
15 |
|
5 |
1 |
5 |
| x |
1 |
1 |
No further division can be done.
Hence, LCM (16, 30) = 240
LCM of 16 and 30 Using Listing the Multiples
To calculate the LCM of 16 and 30 by listing out the common multiples, list the multiples as shown below
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, ……
Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, 240, …..
LCM (16, 30) = 240
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Video Lesson on Applications of LCM
LCM of 16 and 30 Solved Examples
The LCM and GCD of two numbers are 240 and 2 respectively. Find the other number if one number is 30.
Solution:
Consider m as the other number
GCD x LCM = 30 x m
m = (GCD x LCM)/30
m = (2 x 240)/30
m = 16
Hence, the other number is 16.
Frequently Asked Questions on LCM of 16 and 30
Find the LCM of 16 and 30.
What methods can we use to determine the LCM of 16 and 30?
Find the GCF if the LCM of 16 and 30 is 240.
LCM x GCF = 16 x 30
Given
LCM of 16 and 30 = 240
240 x GCF = 480
GCF = 480/240 = 2
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