LCM of 294 and 300
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 294 and 300 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 14700 as output. Here you can check the answer for Find the LCM of 294 and 300.
What is LCM of 294 and 300
Given Numbers are 294, 300
We can find the LCM of 294, 300 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 294 and 300
Multiples of 294 =294,588,882,1176,1470,1764,2058,2352,2646,2940,3234,3528,3822,4116,4410,4704,4998,
Multiples of 300 =300,600,900,1200,1500,1800,2100,2400,2700,3000,3300,3600,3900,4200,4500,4800,5100,
Now, get the least common multiple of 294, 300 which is 14700
So, the LCM of 294, 300 is 14700.
Least Common Multiple (LCM) of 294 and 300 with the help of Prime Factorisation
One method for determining the LCM of 294 and 300 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 294's prime factorization:
| 2 | 294 |
| 3 | 147 |
| 7 | 49 |
| 7 | 7 |
| 1 |
Prime factors of 294 are 2, 3,7.
294 = 21×31×72
And this is 300's prime factorization:
| 2 | 300 |
| 2 | 150 |
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 300 are 2, 3,5.
300 = 22×31×52
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, 3,7,5
.22×31×52×72 = 14700
This shows that the LCM of 294 and 300 is 14700.
How to Calculate the LCM of 294 and 300 Using Common Multiples
The first step in determining the Least Common Multiple of 294 and 300 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 294 and 300:
Lets look at the first ten multiples of these numbers, 294 and 300:
294,588,882,1176,1470,1764,2058,2352,2646,4998 are the first ten multiples of 294.
300,600,900,1200,1500,1800,2100,2400,2700,5100 are the first ten multiples of 300.
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 294 and 300, for example, are 3528, 4998, and 4800. 14700 is the least common multiple since it is the smallest.
294 and 300 have an LCM of 14700.
Least Common Multiple of 294 and 300 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 294 and 300, than apply into the LCM equation.
GCF(294,300) = 6
LCM(294,300) = ( 294 × 300) / 6
LCM(294,300) = 88200 / 6
LCM(294,300) = 14700
Related Least Common Multiples of 294
Related Least Common Multiples of 300
Frequently Asked Questions on LCM of 294 and 300
1. What is the LCM of 294 and 300?
The LCM of 294 and 300 is 14700.
2. How to find the lowest common multiple of 294 and 300?
To find the lowest common multiple of 294 and 300, we have to get the multip;es of both numbers and identify the least common multiple in them which is 14700.
3. What are the Factors of 294?
Answer: Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294. There are 12 integers that are factors of 294. The greatest factor of 294 is 294.
4. What are the Factors of 300?
Answer: Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. There are 18 integers that are factors of 300. The greatest factor of 300 is 300.
5. How to Find the LCM of 294 and 300?Answer:
Least Common Multiple of 294 and 300 = 14700
Step 1: Find the prime factorization of 294
294 = 2 x 3 x 7 x 7
Step 2: Find the prime factorization of 300
300 = 2 x 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 = 14700 = 2 x 2 x 3 x 5 x 5 x 7 x 7
Step 4: Therefore, the least common multiple of 294 and 300 is 14700.