Given Numbers are 380, 384

We can find the LCM of 380, 384 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 380 and 384

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

Multiples of 384 =384,768,1152,1536,1920,2304,2688,3072,3456,3840,4224,4608,4992,5376,5760,6144,6528,

Now, get the least common multiple of 380, 384 which is 36480

So, the LCM of 380, 384 is 36480.

One method for determining the LCM of 380 and 384 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 380's prime factorization:

Prime factors of 380 are 2, 5,19.

380 = 2²×5¹×19¹

And this is 384's prime factorization:

Prime factors of 384 are 2,3.

384 = 2⁷×3¹

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, 5,19,3

2⁷×3¹×5¹×19¹ = 36480

This shows that the LCM of 380 and 384 is 36480.

The first step in determining the Least Common Multiple of 380 and 384 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 380 and 384:

Lets look at the first ten multiples of these numbers, 380 and 384:

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

384,768,1152,1536,1920,2304,2688,3072,3456,6528 are the first ten multiples of 384.

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 380 and 384, for example, are 4560, 6460, and 6144. 36480 is the least common multiple since it is the smallest.

380 and 384 have an LCM of 36480.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 380 and 384, than apply into the LCM equation.

GCF(380,384) = 4
LCM(380,384) = ( 380 × 384) / 4
LCM(380,384) = 145920 / 4
LCM(380,384) = 36480

1. What is the LCM of 380 and 384?

The LCM of 380 and 384 is 36480.

2. How to find the lowest common multiple of 380 and 384?

To find the lowest common multiple of 380 and 384, we have to get the multip;es of both numbers and identify the least common multiple in them which is 36480.

3. 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.

4. What are the Factors of 384?

Answer: Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384. There are 16 integers that are factors of 384. The greatest factor of 384 is 384.

Answer:

Least Common Multiple of 380 and 384 = 36480

Step 1: Find the prime factorization of 380

380 = 2 x 2 x 5 x 19

Step 2: Find the prime factorization of 384

384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

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

LCM = 36480 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 19

Step 4: Therefore, the least common multiple of 380 and 384 is 36480.