Given Numbers are 19, 26

We can find the LCM of 19, 26 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 19 and 26

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

Multiples of 26 =26,52,78,104,130,156,182,208,234,260,286,312,338,364,390,416,442,

Now, get the least common multiple of 19, 26 which is 494

So, the LCM of 19, 26 is 494.

One method for determining the LCM of 19 and 26 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 26's prime factorization:

Prime factors of 26 are 2,13.

26 = 2¹×13¹

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, 2,13

2¹×13¹×19¹ = 494

This shows that the LCM of 19 and 26 is 494.

The first step in determining the Least Common Multiple of 19 and 26 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 19 and 26:

Lets look at the first ten multiples of these numbers, 19 and 26:

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

26,52,78,104,130,156,182,208,234,442 are the first ten multiples of 26.

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 26, for example, are 228, 323, and 416. 494 is the least common multiple since it is the smallest.

19 and 26 have an LCM of 494.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 26, than apply into the LCM equation.

GCF(19,26) = 1
LCM(19,26) = ( 19 × 26) / 1
LCM(19,26) = 494 / 1
LCM(19,26) = 494

1. What is the LCM of 19 and 26?

The LCM of 19 and 26 is 494.

2. How to find the lowest common multiple of 19 and 26?

To find the lowest common multiple of 19 and 26, we have to get the multip;es of both numbers and identify the least common multiple in them which is 494.

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 26?

Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.

Answer:

Least Common Multiple of 19 and 26 = 494

Step 1: Find the prime factorization of 19

19 = 19

Step 2: Find the prime factorization of 26

26 = 2 x 13

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

LCM = 494 = 2 x 13 x 19

Step 4: Therefore, the least common multiple of 19 and 26 is 494.