Least Common Multiple of 19 and 26

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 19 and 26 by Prime method
• Least Common Multiple of 19 and 26 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 19 and 26. First we will calculate the prime factors of 19 and 26.

Prime Factorization of 19

Prime factors of 19 are 19. Prime factorization of 19 in exponential form is:

19 = 19¹

Prime Factorization of 26

Prime factors of 26 are 2,13. Prime factorization of 26 in exponential form is:

26 = 2¹×13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 19 and 26.

LCM(19,26) = 2¹×13¹×19¹
LCM(19,26) = 494

Factors of 19

List of positive integer factors of 19 that divides 19 without a remainder.

1, 19

Factors of 26

List of positive integer factors of 26 that divides 26 without a remainder.

1, 2, 13, 26

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

(i) The LCM of 26 and 19 is associative

LCM of 19 and 26 = LCM of 26 and 19

1. What is the LCM of 19 and 26?

Answer: LCM of 19 and 26 is 494.

2. 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.

3. 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.

4. How to Find the LCM of 19 and 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.