Given Numbers are 34, 38

We can find the LCM of 34, 38 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 34 and 38

Multiples of 34 =34,68,102,136,170,204,238,272,306,340,374,408,442,476,510,544,578,

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 34, 38 which is 646

So, the LCM of 34, 38 is 646.

One method for determining the LCM of 34 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 34's prime factorization:

Prime factors of 34 are 2,17.

34 = 2¹×17¹

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: 2,17,19

2¹×17¹×19¹ = 646

This shows that the LCM of 34 and 38 is 646.

The first step in determining the Least Common Multiple of 34 and 38 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 34 and 38:

Lets look at the first ten multiples of these numbers, 34 and 38:

34,68,102,136,170,204,238,272,306,578 are the first ten multiples of 34.

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 34 and 38, for example, are 408, 578, and 608. 646 is the least common multiple since it is the smallest.

34 and 38 have an LCM of 646.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 38, than apply into the LCM equation.

GCF(34,38) = 2
LCM(34,38) = ( 34 × 38) / 2
LCM(34,38) = 1292 / 2
LCM(34,38) = 646

1. What is the LCM of 34 and 38?

The LCM of 34 and 38 is 646.

2. How to find the lowest common multiple of 34 and 38?

To find the lowest common multiple of 34 and 38, we have to get the multip;es of both numbers and identify the least common multiple in them which is 646.

3. What are the Factors of 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

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 34 and 38 = 646

Step 1: Find the prime factorization of 34

34 = 2 x 17

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 = 646 = 2 x 17 x 19

Step 4: Therefore, the least common multiple of 34 and 38 is 646.