LCM of 369 and 374
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 369 and 374 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 138006 as output. Here you can check the answer for Find the LCM of 369 and 374.
What is LCM of 369 and 374
Given Numbers are 369, 374
We can find the LCM of 369, 374 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 369 and 374
Multiples of 369 =369,738,1107,1476,1845,2214,2583,2952,3321,3690,4059,4428,4797,5166,5535,5904,6273,
Multiples of 374 =374,748,1122,1496,1870,2244,2618,2992,3366,3740,4114,4488,4862,5236,5610,5984,6358,
Now, get the least common multiple of 369, 374 which is 138006
So, the LCM of 369, 374 is 138006.
Least Common Multiple (LCM) of 369 and 374 with the help of Prime Factorisation
One method for determining the LCM of 369 and 374 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 369's prime factorization:
| 3 | 369 |
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 369 are 3,41.
369 = 32×411
And this is 374's prime factorization:
| 2 | 374 |
| 11 | 187 |
| 17 | 17 |
| 1 |
Prime factors of 374 are 2, 11,17.
374 = 21×111×171
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: 3,41, 2, 11,17
.21×32×111×171×411 = 138006
This shows that the LCM of 369 and 374 is 138006.
How to Calculate the LCM of 369 and 374 Using Common Multiples
The first step in determining the Least Common Multiple of 369 and 374 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 369 and 374:
Lets look at the first ten multiples of these numbers, 369 and 374:
369,738,1107,1476,1845,2214,2583,2952,3321,6273 are the first ten multiples of 369.
374,748,1122,1496,1870,2244,2618,2992,3366,6358 are the first ten multiples of 374.
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 369 and 374, for example, are 4428, 6273, and 5984. 138006 is the least common multiple since it is the smallest.
369 and 374 have an LCM of 138006.
Least Common Multiple of 369 and 374 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 369 and 374, than apply into the LCM equation.
GCF(369,374) = 1
LCM(369,374) = ( 369 × 374) / 1
LCM(369,374) = 138006 / 1
LCM(369,374) = 138006
Related Least Common Multiples of 369
Related Least Common Multiples of 374
Frequently Asked Questions on LCM of 369 and 374
1. What is the LCM of 369 and 374?
The LCM of 369 and 374 is 138006.
2. How to find the lowest common multiple of 369 and 374?
To find the lowest common multiple of 369 and 374, we have to get the multip;es of both numbers and identify the least common multiple in them which is 138006.
3. What are the Factors of 369?
Answer: Factors of 369 are 1, 3, 9, 41, 123, 369. There are 6 integers that are factors of 369. The greatest factor of 369 is 369.
4. What are the Factors of 374?
Answer: Factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374. There are 8 integers that are factors of 374. The greatest factor of 374 is 374.
5. How to Find the LCM of 369 and 374?Answer:
Least Common Multiple of 369 and 374 = 138006
Step 1: Find the prime factorization of 369
369 = 3 x 3 x 41
Step 2: Find the prime factorization of 374
374 = 2 x 11 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 138006 = 2 x 3 x 3 x 11 x 17 x 41
Step 4: Therefore, the least common multiple of 369 and 374 is 138006.