LCM of 150 and 180 is 900. Get a good knowledge of the least common multiple of 150 and 180 referring to this article designed by the subject experts. The multiples of 150 are (150, 300, 450, 600, ….) and the multiples of 180 are (180, 360, 540, 720, 900, 1080,….). The LCM of two numbers according to prime factorisation, by listing out the multiples and division, is explained here in brief.
Also read: Least common multiple
What is LCM of 150 and 180?
The answer to this question is 900. The LCM of 150 and 180 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 150 and 180, is the smallest positive integer 900 which is divisible by both 150 and 180 with no remainder.
How to Find LCM of 150 and 180?
LCM of 150 and 180 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 150 and 180 Using Prime Factorisation Method
The prime factorisation of 150 and 180, respectively, is given by:
150 = 2 x 3 x 5 x 5 = 2¹x 3¹ x 5²
180 = 2 x 2 x 3 x 3 x 5 = 2² x 3² x 5¹
LCM (150, 180) = 900
LCM of 150 and 180 Using Division Method
We’ll divide the numbers (150, 180) by their prime factors to get the LCM of 150 and 180 using the division method (preferably common). The LCM of 150 and 180 is calculated by multiplying these divisors.
|
2 |
150 |
180 |
|
2 |
75 |
90 |
|
3 |
75 |
45 |
|
3 |
25 |
15 |
|
5 |
25 |
5 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (150, 180) = 900
LCM of 150 and 180 Using Listing the Multiples
To calculate the LCM of 150 and 180 by listing out the common multiples, list the multiples as shown below
|
Multiples of 150 |
Multiples of 180 |
|
150 |
180 |
|
300 |
360 |
|
450 |
540 |
|
600 |
720 |
|
750 |
900 |
|
900 |
1080 |
The smallest common multiple of 150 and 180 is 900.
Therefore LCM (150, 180) = 900
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 150 and 180 Solved Examples
Question: If the GCD = 30, LCM = 900 and one number is 150, determine the other.
Solution:
Consider z as the other number
GCD x LCM = 150 x z
z = (GCD x LCM)/150
z = (30 x 900)/150
z = 180
Hence, the LCM is 180.
Frequently Asked Questions on LCM of 150 and 180
What is the LCM of 150 and 180?
Write the methods used to get the LCM of 150 and 180.
Determine the GCF if the LCM of 150 and 180 is 900.
LCM x GCF = 150 x 180
Given
LCM of 150 and 180 = 900
900 x GCF = 27000
GCF = 27000/900 = 30
Find the LCM of 150 and 180 with the help of prime factorisation.
With the help of prime factorisation
150 = 2 x 3 x 5 x 5
180 = 2 x 2 x 3 x 3 x 5
LCM of 150 and 180 is 900.
Write the relation between GCF and LCM of 150 and 180.
The relation between GCF and LCM of 150 and 180 is
GCF x LCM = 150 x 180
GCF x LCM = 27000
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