Given Numbers are 32, 38

We can find the LCM of 32, 38 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 32 and 38

Multiples of 32 =32,64,96,128,160,192,224,256,288,320,352,384,416,448,480,512,544,

Multiples of 38 =38,76,114,152,190,228,266,304,342,380,418,456,494,532,570,608,646,

Now, get the least common multiple of 32, 38 which is 608

So, the LCM of 32, 38 is 608.

One method for determining the LCM of 32 and 38 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 32's prime factorization:

Prime factors of 32 are 2.

32 = 2⁵

And this is 38's prime factorization:

Prime factors of 38 are 2,19.

38 = 2¹×19¹

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:2,19

2⁵×19¹ = 608

This shows that the LCM of 32 and 38 is 608.

The first step in determining the Least Common Multiple of 32 and 38 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 32 and 38:

Lets look at the first ten multiples of these numbers, 32 and 38:

32,64,96,128,160,192,224,256,288,544 are the first ten multiples of 32.

38,76,114,152,190,228,266,304,342,646 are the first ten multiples of 38.

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 32 and 38, for example, are 384, 544, and 608. 608 is the least common multiple since it is the smallest.

32 and 38 have an LCM of 608.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32 and 38, than apply into the LCM equation.

GCF(32,38) = 2
LCM(32,38) = ( 32 × 38) / 2
LCM(32,38) = 1216 / 2
LCM(32,38) = 608

1. What is the LCM of 32 and 38?

The LCM of 32 and 38 is 608.

2. How to find the lowest common multiple of 32 and 38?

To find the lowest common multiple of 32 and 38, we have to get the multip;es of both numbers and identify the least common multiple in them which is 608.

3. What are the Factors of 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

4. What are the Factors of 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

Answer:

Least Common Multiple of 32 and 38 = 608

Step 1: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 38

38 = 2 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 = 608 = 2 x 2 x 2 x 2 x 2 x 19

Step 4: Therefore, the least common multiple of 32 and 38 is 608.