LCM of 354 and 360
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 354 and 360 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 21240 as output. Here you can check the answer for Find the LCM of 354 and 360.
What is LCM of 354 and 360
Given Numbers are 354, 360
We can find the LCM of 354, 360 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 354 and 360
Multiples of 354 =354,708,1062,1416,1770,2124,2478,2832,3186,3540,3894,4248,4602,4956,5310,5664,6018,
Multiples of 360 =360,720,1080,1440,1800,2160,2520,2880,3240,3600,3960,4320,4680,5040,5400,5760,6120,
Now, get the least common multiple of 354, 360 which is 21240
So, the LCM of 354, 360 is 21240.
Least Common Multiple (LCM) of 354 and 360 with the help of Prime Factorisation
One method for determining the LCM of 354 and 360 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 354's prime factorization:
| 2 | 354 |
| 3 | 177 |
| 59 | 59 |
| 1 |
Prime factors of 354 are 2, 3,59.
354 = 21×31×591
And this is 360's prime factorization:
| 2 | 360 |
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 360 are 2, 3,5.
360 = 23×32×51
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, 3,59,5
.23×32×51×591 = 21240
This shows that the LCM of 354 and 360 is 21240.
How to Calculate the LCM of 354 and 360 Using Common Multiples
The first step in determining the Least Common Multiple of 354 and 360 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 354 and 360:
Lets look at the first ten multiples of these numbers, 354 and 360:
354,708,1062,1416,1770,2124,2478,2832,3186,6018 are the first ten multiples of 354.
360,720,1080,1440,1800,2160,2520,2880,3240,6120 are the first ten multiples of 360.
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 354 and 360, for example, are 4248, 6018, and 5760. 21240 is the least common multiple since it is the smallest.
354 and 360 have an LCM of 21240.
Least Common Multiple of 354 and 360 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 354 and 360, than apply into the LCM equation.
GCF(354,360) = 6
LCM(354,360) = ( 354 × 360) / 6
LCM(354,360) = 127440 / 6
LCM(354,360) = 21240
Related Least Common Multiples of 354
Related Least Common Multiples of 360
Frequently Asked Questions on LCM of 354 and 360
1. What is the LCM of 354 and 360?
The LCM of 354 and 360 is 21240.
2. How to find the lowest common multiple of 354 and 360?
To find the lowest common multiple of 354 and 360, we have to get the multip;es of both numbers and identify the least common multiple in them which is 21240.
3. What are the Factors of 354?
Answer: Factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354. There are 8 integers that are factors of 354. The greatest factor of 354 is 354.
4. What are the Factors of 360?
Answer: Factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. There are 24 integers that are factors of 360. The greatest factor of 360 is 360.
5. How to Find the LCM of 354 and 360?Answer:
Least Common Multiple of 354 and 360 = 21240
Step 1: Find the prime factorization of 354
354 = 2 x 3 x 59
Step 2: Find the prime factorization of 360
360 = 2 x 2 x 2 x 3 x 3 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 = 21240 = 2 x 2 x 2 x 3 x 3 x 5 x 59
Step 4: Therefore, the least common multiple of 354 and 360 is 21240.