Given Numbers are 374, 380

We can find the LCM of 374, 380 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 374 and 380

Multiples of 374 =374,748,1122,1496,1870,2244,2618,2992,3366,3740,4114,4488,4862,5236,5610,5984,6358,

Multiples of 380 =380,760,1140,1520,1900,2280,2660,3040,3420,3800,4180,4560,4940,5320,5700,6080,6460,

Now, get the least common multiple of 374, 380 which is 71060

So, the LCM of 374, 380 is 71060.

One method for determining the LCM of 374 and 380 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 374's prime factorization:

Prime factors of 374 are 2, 11,17.

374 = 2¹×11¹×17¹

And this is 380's prime factorization:

Prime factors of 380 are 2, 5,19.

380 = 2²×5¹×19¹

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, 11,17, 5,19

2²×5¹×11¹×17¹×19¹ = 71060

This shows that the LCM of 374 and 380 is 71060.

The first step in determining the Least Common Multiple of 374 and 380 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 374 and 380:

Lets look at the first ten multiples of these numbers, 374 and 380:

374,748,1122,1496,1870,2244,2618,2992,3366,6358 are the first ten multiples of 374.

380,760,1140,1520,1900,2280,2660,3040,3420,6460 are the first ten multiples of 380.

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 374 and 380, for example, are 4488, 6358, and 6080. 71060 is the least common multiple since it is the smallest.

374 and 380 have an LCM of 71060.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 374 and 380, than apply into the LCM equation.

GCF(374,380) = 2
LCM(374,380) = ( 374 × 380) / 2
LCM(374,380) = 142120 / 2
LCM(374,380) = 71060

1. What is the LCM of 374 and 380?

The LCM of 374 and 380 is 71060.

2. How to find the lowest common multiple of 374 and 380?

To find the lowest common multiple of 374 and 380, we have to get the multip;es of both numbers and identify the least common multiple in them which is 71060.

3. 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.

4. What are the Factors of 380?

Answer: Factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380. There are 12 integers that are factors of 380. The greatest factor of 380 is 380.

Answer:

Least Common Multiple of 374 and 380 = 71060

Step 1: Find the prime factorization of 374

374 = 2 x 11 x 17

Step 2: Find the prime factorization of 380

380 = 2 x 2 x 5 x 19

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 71060 = 2 x 2 x 5 x 11 x 17 x 19

Step 4: Therefore, the least common multiple of 374 and 380 is 71060.