LCM of 324 and 330
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 324 and 330 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 17820 as output. Here you can check the answer for Find the LCM of 324 and 330.
What is LCM of 324 and 330
Given Numbers are 324, 330
We can find the LCM of 324, 330 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 324 and 330
Multiples of 324 =324,648,972,1296,1620,1944,2268,2592,2916,3240,3564,3888,4212,4536,4860,5184,5508,
Multiples of 330 =330,660,990,1320,1650,1980,2310,2640,2970,3300,3630,3960,4290,4620,4950,5280,5610,
Now, get the least common multiple of 324, 330 which is 17820
So, the LCM of 324, 330 is 17820.
Least Common Multiple (LCM) of 324 and 330 with the help of Prime Factorisation
One method for determining the LCM of 324 and 330 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 324's prime factorization:
| 2 | 324 |
| 2 | 162 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 324 are 2,3.
324 = 22×34
And this is 330's prime factorization:
| 2 | 330 |
| 3 | 165 |
| 5 | 55 |
| 11 | 11 |
| 1 |
Prime factors of 330 are 2, 3, 5,11.
330 = 21×31×51×111
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, 5,11
.22×34×51×111 = 17820
This shows that the LCM of 324 and 330 is 17820.
How to Calculate the LCM of 324 and 330 Using Common Multiples
The first step in determining the Least Common Multiple of 324 and 330 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 324 and 330:
Lets look at the first ten multiples of these numbers, 324 and 330:
324,648,972,1296,1620,1944,2268,2592,2916,5508 are the first ten multiples of 324.
330,660,990,1320,1650,1980,2310,2640,2970,5610 are the first ten multiples of 330.
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 324 and 330, for example, are 3888, 5508, and 5280. 17820 is the least common multiple since it is the smallest.
324 and 330 have an LCM of 17820.
Least Common Multiple of 324 and 330 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 324 and 330, than apply into the LCM equation.
GCF(324,330) = 6
LCM(324,330) = ( 324 × 330) / 6
LCM(324,330) = 106920 / 6
LCM(324,330) = 17820
Related Least Common Multiples of 324
Related Least Common Multiples of 330
Frequently Asked Questions on LCM of 324 and 330
1. What is the LCM of 324 and 330?
The LCM of 324 and 330 is 17820.
2. How to find the lowest common multiple of 324 and 330?
To find the lowest common multiple of 324 and 330, we have to get the multip;es of both numbers and identify the least common multiple in them which is 17820.
3. What are the Factors of 324?
Answer: Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324. There are 15 integers that are factors of 324. The greatest factor of 324 is 324.
4. What are the Factors of 330?
Answer: Factors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330. There are 16 integers that are factors of 330. The greatest factor of 330 is 330.
5. How to Find the LCM of 324 and 330?Answer:
Least Common Multiple of 324 and 330 = 17820
Step 1: Find the prime factorization of 324
324 = 2 x 2 x 3 x 3 x 3 x 3
Step 2: Find the prime factorization of 330
330 = 2 x 3 x 5 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 17820 = 2 x 2 x 3 x 3 x 3 x 3 x 5 x 11
Step 4: Therefore, the least common multiple of 324 and 330 is 17820.