Least Common Multiple of 9 and 19

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 9 and 19 the smallest integer that is 171 that is divisible by both numbers.

Least Common Multiple (LCM) of 9 and 19 is 171.

LCM(9,19) = 171

LCM of 9 and 19

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

LCM of:
and

Least Common Multiple of 9 and 19

LCM of 9 and 19 is 171

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 19. First we will calculate the prime factors of 9 and 19.

Prime Factorization of 9


3 9
3 3
1

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 32

Prime Factorization of 19


19 19
1

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 9 and 19.

LCM(9,19) = 32×191
LCM(9,19) = 171

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

Factors of 19

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

1, 19

Least Common Multiple of 9 and 19 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 19, than apply into the LCM equation.

GCF(9,19) = 1
LCM(9,19) = ( 9 × 19) / 1
LCM(9,19) = 171 / 1
LCM(9,19) = 171

Properties of LCM 9 and 19

(i) The LCM of 19 and 9 is associative

LCM of 9 and 19 = LCM of 19 and 9

Frequently Asked Questions on LCM of 9 and 19

1. What is the LCM of 9 and 19?

Answer: LCM of 9 and 19 is 171.

2. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

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 9 and 19?

Answer:

Least Common Multiple of 9 and 19 = 171

Step 1: Find the prime factorization of 9

9 = 3 x 3

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 = 171 = 3 x 3 x 19

Step 4: Therefore, the least common multiple of 9 and 19 is 171.