LCM of 140 and 144
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 140 and 144 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 5040 as output. Here you can check the answer for Find the LCM of 140 and 144.
What is LCM of 140 and 144
Given Numbers are 140, 144
We can find the LCM of 140, 144 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 140 and 144
Multiples of 140 =140,280,420,560,700,840,980,1120,1260,1400,1540,1680,1820,1960,2100,2240,2380,
Multiples of 144 =144,288,432,576,720,864,1008,1152,1296,1440,1584,1728,1872,2016,2160,2304,2448,
Now, get the least common multiple of 140, 144 which is 5040
So, the LCM of 140, 144 is 5040.
Least Common Multiple (LCM) of 140 and 144 with the help of Prime Factorisation
One method for determining the LCM of 140 and 144 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 140's prime factorization:
| 2 | 140 |
| 2 | 70 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 140 are 2, 5,7.
140 = 22×51×71
And this 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
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, 5,7,3
.24×32×51×71 = 5040
This shows that the LCM of 140 and 144 is 5040.
How to Calculate the LCM of 140 and 144 Using Common Multiples
The first step in determining the Least Common Multiple of 140 and 144 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 140 and 144:
Lets look at the first ten multiples of these numbers, 140 and 144:
140,280,420,560,700,840,980,1120,1260,2380 are the first ten multiples of 140.
144,288,432,576,720,864,1008,1152,1296,2448 are the first ten multiples of 144.
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 140 and 144, for example, are 1680, 2380, and 2304. 5040 is the least common multiple since it is the smallest.
140 and 144 have an LCM of 5040.
Least Common Multiple of 140 and 144 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 140 and 144, than apply into the LCM equation.
GCF(140,144) = 4
LCM(140,144) = ( 140 × 144) / 4
LCM(140,144) = 20160 / 4
LCM(140,144) = 5040
Related Least Common Multiples of 140
Related Least Common Multiples of 144
Frequently Asked Questions on LCM of 140 and 144
1. What is the LCM of 140 and 144?
The LCM of 140 and 144 is 5040.
2. How to find the lowest common multiple of 140 and 144?
To find the lowest common multiple of 140 and 144, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5040.
3. What are the Factors of 140?
Answer: Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. There are 12 integers that are factors of 140. The greatest factor of 140 is 140.
4. 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.
5. How to Find the LCM of 140 and 144?Answer:
Least Common Multiple of 140 and 144 = 5040
Step 1: Find the prime factorization of 140
140 = 2 x 2 x 5 x 7
Step 2: Find the prime factorization of 144
144 = 2 x 2 x 2 x 2 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 140 and 144 is 5040.