Least Common Multiple of 6 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 6 and 19 the smallest integer that is 114 that is divisible by both numbers.

Least Common Multiple (LCM) of 6 and 19 is 114.

LCM(6,19) = 114

LCM of 6 and 19

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

LCM of:
and

Least Common Multiple of 6 and 19

LCM of 6 and 19 is 114

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 19. First we will calculate the prime factors of 6 and 19.

Prime Factorization of 6


2 6
3 3
1

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 21×31

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 6 and 19.

LCM(6,19) = 21×31×191
LCM(6,19) = 114

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3, 6

Factors of 19

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

1, 19

Least Common Multiple of 6 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 6 and 19, than apply into the LCM equation.

GCF(6,19) = 1
LCM(6,19) = ( 6 × 19) / 1
LCM(6,19) = 114 / 1
LCM(6,19) = 114

Properties of LCM 6 and 19

(i) The LCM of 19 and 6 is associative

LCM of 6 and 19 = LCM of 19 and 6

Frequently Asked Questions on LCM of 6 and 19

1. What is the LCM of 6 and 19?

Answer: LCM of 6 and 19 is 114.

2. What are the Factors of 6?

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

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 6 and 19?

Answer:

Least Common Multiple of 6 and 19 = 114

Step 1: Find the prime factorization of 6

6 = 2 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 = 114 = 2 x 3 x 19

Step 4: Therefore, the least common multiple of 6 and 19 is 114.