LCM of 144 and 148
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 144 and 148 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 5328 as output. Here you can check the answer for Find the LCM of 144 and 148.
What is LCM of 144 and 148
Given Numbers are 144, 148
We can find the LCM of 144, 148 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 144 and 148
Multiples of 144 =144,288,432,576,720,864,1008,1152,1296,1440,1584,1728,1872,2016,2160,2304,2448,
Multiples of 148 =148,296,444,592,740,888,1036,1184,1332,1480,1628,1776,1924,2072,2220,2368,2516,
Now, get the least common multiple of 144, 148 which is 5328
So, the LCM of 144, 148 is 5328.
Least Common Multiple (LCM) of 144 and 148 with the help of Prime Factorisation
One method for determining the LCM of 144 and 148 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 148's prime factorization:
| 2 | 148 |
| 2 | 74 |
| 37 | 37 |
| 1 |
Prime factors of 148 are 2,37.
148 = 22×371
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: 2,3,37
.24×32×371 = 5328
This shows that the LCM of 144 and 148 is 5328.
How to Calculate the LCM of 144 and 148 Using Common Multiples
The first step in determining the Least Common Multiple of 144 and 148 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 144 and 148:
Lets look at the first ten multiples of these numbers, 144 and 148:
144,288,432,576,720,864,1008,1152,1296,2448 are the first ten multiples of 144.
148,296,444,592,740,888,1036,1184,1332,2516 are the first ten multiples of 148.
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 148, for example, are 1728, 2448, and 2368. 5328 is the least common multiple since it is the smallest.
144 and 148 have an LCM of 5328.
Least Common Multiple of 144 and 148 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 148, than apply into the LCM equation.
GCF(144,148) = 4
LCM(144,148) = ( 144 × 148) / 4
LCM(144,148) = 21312 / 4
LCM(144,148) = 5328
Related Least Common Multiples of 144
Related Least Common Multiples of 148
Frequently Asked Questions on LCM of 144 and 148
1. What is the LCM of 144 and 148?
The LCM of 144 and 148 is 5328.
2. How to find the lowest common multiple of 144 and 148?
To find the lowest common multiple of 144 and 148, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5328.
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 148?
Answer: Factors of 148 are 1, 2, 4, 37, 74, 148. There are 6 integers that are factors of 148. The greatest factor of 148 is 148.
5. How to Find the LCM of 144 and 148?Answer:
Least Common Multiple of 144 and 148 = 5328
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 148
148 = 2 x 2 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5328 = 2 x 2 x 2 x 2 x 3 x 3 x 37
Step 4: Therefore, the least common multiple of 144 and 148 is 5328.