Given Numbers are 19, 24

We can find the LCM of 19, 24 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 19 and 24

Multiples of 19 =19,38,57,76,95,114,133,152,171,190,209,228,247,266,285,304,323,

Multiples of 24 =24,48,72,96,120,144,168,192,216,240,264,288,312,336,360,384,408,

Now, get the least common multiple of 19, 24 which is 456

So, the LCM of 19, 24 is 456.

One method for determining the LCM of 19 and 24 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 19's prime factorization:

Prime factors of 19 are 19.

19 = 19¹

And this is 24's prime factorization:

Prime factors of 24 are 2,3.

24 = 2³×3¹

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:19, 2,3

2³×3¹×19¹ = 456

This shows that the LCM of 19 and 24 is 456.

The first step in determining the Least Common Multiple of 19 and 24 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 19 and 24:

Lets look at the first ten multiples of these numbers, 19 and 24:

19,38,57,76,95,114,133,152,171,323 are the first ten multiples of 19.

24,48,72,96,120,144,168,192,216,408 are the first ten multiples of 24.

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 19 and 24, for example, are 228, 323, and 384. 456 is the least common multiple since it is the smallest.

19 and 24 have an LCM of 456.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 24, than apply into the LCM equation.

GCF(19,24) = 1
LCM(19,24) = ( 19 × 24) / 1
LCM(19,24) = 456 / 1
LCM(19,24) = 456

1. What is the LCM of 19 and 24?

The LCM of 19 and 24 is 456.

2. How to find the lowest common multiple of 19 and 24?

To find the lowest common multiple of 19 and 24, we have to get the multip;es of both numbers and identify the least common multiple in them which is 456.

3. What are the Factors of 19?

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

4. What are the Factors of 24?

Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.

Answer:

Least Common Multiple of 19 and 24 = 456

Step 1: Find the prime factorization of 19

19 = 19

Step 2: Find the prime factorization of 24

24 = 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 = 456 = 2 x 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 19 and 24 is 456.