LCM of 144 and 150
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 144 and 150 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3600 as output. Here you can check the answer for Find the LCM of 144 and 150.
What is LCM of 144 and 150
Given Numbers are 144, 150
We can find the LCM of 144, 150 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 144 and 150
Multiples of 144 =144,288,432,576,720,864,1008,1152,1296,1440,1584,1728,1872,2016,2160,2304,2448,
Multiples of 150 =150,300,450,600,750,900,1050,1200,1350,1500,1650,1800,1950,2100,2250,2400,2550,
Now, get the least common multiple of 144, 150 which is 3600
So, the LCM of 144, 150 is 3600.
Least Common Multiple (LCM) of 144 and 150 with the help of Prime Factorisation
One method for determining the LCM of 144 and 150 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 144's prime factorization:
| 2 | 144 |
| 2 | 72 |
| 2 | 36 |
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 144 are 2,3.
144 = 24×32
And this is 150's prime factorization:
| 2 | 150 |
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 150 are 2, 3,5.
150 = 21×31×52
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2,3,5
.24×32×52 = 3600
This shows that the LCM of 144 and 150 is 3600.
How to Calculate the LCM of 144 and 150 Using Common Multiples
The first step in determining the Least Common Multiple of 144 and 150 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 144 and 150:
Lets look at the first ten multiples of these numbers, 144 and 150:
144,288,432,576,720,864,1008,1152,1296,2448 are the first ten multiples of 144.
150,300,450,600,750,900,1050,1200,1350,2550 are the first ten multiples of 150.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 144 and 150, for example, are 1728, 2448, and 2400. 3600 is the least common multiple since it is the smallest.
144 and 150 have an LCM of 3600.
Least Common Multiple of 144 and 150 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 144 and 150, than apply into the LCM equation.
GCF(144,150) = 6
LCM(144,150) = ( 144 × 150) / 6
LCM(144,150) = 21600 / 6
LCM(144,150) = 3600
Related Least Common Multiples of 144
Related Least Common Multiples of 150
Frequently Asked Questions on LCM of 144 and 150
1. What is the LCM of 144 and 150?
The LCM of 144 and 150 is 3600.
2. How to find the lowest common multiple of 144 and 150?
To find the lowest common multiple of 144 and 150, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3600.
3. What are the Factors of 144?
Answer: Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. There are 15 integers that are factors of 144. The greatest factor of 144 is 144.
4. What are the Factors of 150?
Answer: Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150. There are 12 integers that are factors of 150. The greatest factor of 150 is 150.
5. How to Find the LCM of 144 and 150?Answer:
Least Common Multiple of 144 and 150 = 3600
Step 1: Find the prime factorization of 144
144 = 2 x 2 x 2 x 2 x 3 x 3
Step 2: Find the prime factorization of 150
150 = 2 x 3 x 5 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5
Step 4: Therefore, the least common multiple of 144 and 150 is 3600.