Given Numbers are 57, 64

We can find the LCM of 57, 64 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 57 and 64

Multiples of 57 =57,114,171,228,285,342,399,456,513,570,627,684,741,798,855,912,969,

Multiples of 64 =64,128,192,256,320,384,448,512,576,640,704,768,832,896,960,1024,1088,

Now, get the least common multiple of 57, 64 which is 3648

So, the LCM of 57, 64 is 3648.

One method for determining the LCM of 57 and 64 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 57's prime factorization:

Prime factors of 57 are 3,19.

57 = 3¹×19¹

And this is 64's prime factorization:

Prime factors of 64 are 2.

64 = 2⁶

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: 3,19,2

2⁶×3¹×19¹ = 3648

This shows that the LCM of 57 and 64 is 3648.

The first step in determining the Least Common Multiple of 57 and 64 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 57 and 64:

Lets look at the first ten multiples of these numbers, 57 and 64:

57,114,171,228,285,342,399,456,513,969 are the first ten multiples of 57.

64,128,192,256,320,384,448,512,576,1088 are the first ten multiples of 64.

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 57 and 64, for example, are 684, 969, and 1024. 3648 is the least common multiple since it is the smallest.

57 and 64 have an LCM of 3648.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57 and 64, than apply into the LCM equation.

GCF(57,64) = 1
LCM(57,64) = ( 57 × 64) / 1
LCM(57,64) = 3648 / 1
LCM(57,64) = 3648

1. What is the LCM of 57 and 64?

The LCM of 57 and 64 is 3648.

2. How to find the lowest common multiple of 57 and 64?

To find the lowest common multiple of 57 and 64, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3648.

3. What are the Factors of 57?

Answer: Factors of 57 are 1, 3, 19, 57. There are 4 integers that are factors of 57. The greatest factor of 57 is 57.

4. What are the Factors of 64?

Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.

Answer:

Least Common Multiple of 57 and 64 = 3648

Step 1: Find the prime factorization of 57

57 = 3 x 19

Step 2: Find the prime factorization of 64

64 = 2 x 2 x 2 x 2 x 2 x 2

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

LCM = 3648 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 57 and 64 is 3648.