Given Numbers are 364, 370

We can find the LCM of 364, 370 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 364 and 370

Multiples of 364 =364,728,1092,1456,1820,2184,2548,2912,3276,3640,4004,4368,4732,5096,5460,5824,6188,

Multiples of 370 =370,740,1110,1480,1850,2220,2590,2960,3330,3700,4070,4440,4810,5180,5550,5920,6290,

Now, get the least common multiple of 364, 370 which is 67340

So, the LCM of 364, 370 is 67340.

One method for determining the LCM of 364 and 370 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 364's prime factorization:

Prime factors of 364 are 2, 7,13.

364 = 2²×7¹×13¹

And this is 370's prime factorization:

Prime factors of 370 are 2, 5,37.

370 = 2¹×5¹×37¹

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, 7,13, 5,37

2²×5¹×7¹×13¹×37¹ = 67340

This shows that the LCM of 364 and 370 is 67340.

The first step in determining the Least Common Multiple of 364 and 370 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 364 and 370:

Lets look at the first ten multiples of these numbers, 364 and 370:

364,728,1092,1456,1820,2184,2548,2912,3276,6188 are the first ten multiples of 364.

370,740,1110,1480,1850,2220,2590,2960,3330,6290 are the first ten multiples of 370.

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 364 and 370, for example, are 4368, 6188, and 5920. 67340 is the least common multiple since it is the smallest.

364 and 370 have an LCM of 67340.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 364 and 370, than apply into the LCM equation.

GCF(364,370) = 2
LCM(364,370) = ( 364 × 370) / 2
LCM(364,370) = 134680 / 2
LCM(364,370) = 67340

1. What is the LCM of 364 and 370?

The LCM of 364 and 370 is 67340.

2. How to find the lowest common multiple of 364 and 370?

To find the lowest common multiple of 364 and 370, we have to get the multip;es of both numbers and identify the least common multiple in them which is 67340.

3. What are the Factors of 364?

Answer: Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364. There are 12 integers that are factors of 364. The greatest factor of 364 is 364.

4. What are the Factors of 370?

Answer: Factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370. There are 8 integers that are factors of 370. The greatest factor of 370 is 370.

Answer:

Least Common Multiple of 364 and 370 = 67340

Step 1: Find the prime factorization of 364

364 = 2 x 2 x 7 x 13

Step 2: Find the prime factorization of 370

370 = 2 x 5 x 37

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

LCM = 67340 = 2 x 2 x 5 x 7 x 13 x 37

Step 4: Therefore, the least common multiple of 364 and 370 is 67340.