Least Common Multiple of 10 and 19

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

• Least Common Multiple of 10 and 19 by Prime method
• Least Common Multiple of 10 and 19 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 19. First we will calculate the prime factors of 10 and 19.

Prime Factorization of 10

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 2¹×5¹

Prime Factorization of 19

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

19 = 19¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 19.

LCM(10,19) = 2¹×5¹×19¹
LCM(10,19) = 190

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Factors of 19

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

1, 19

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 19, than apply into the LCM equation.

GCF(10,19) = 1
LCM(10,19) = ( 10 × 19) / 1
LCM(10,19) = 190 / 1
LCM(10,19) = 190

(i) The LCM of 19 and 10 is associative

LCM of 10 and 19 = LCM of 19 and 10

1. What is the LCM of 10 and 19?

Answer: LCM of 10 and 19 is 190.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

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. How to Find the LCM of 10 and 19?

Answer:

Least Common Multiple of 10 and 19 = 190

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 19

19 = 19

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

LCM = 190 = 2 x 5 x 19

Step 4: Therefore, the least common multiple of 10 and 19 is 190.