Least Common Multiple of 19 and 24

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 19 and 24 the smallest integer that is 456 that is divisible by both numbers.

Least Common Multiple (LCM) of 19 and 24 is 456.

LCM(19,24) = 456

LCM of 19 and 24

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

LCM of:
and

Least Common Multiple of 19 and 24

LCM of 19 and 24 is 456

Least common multiple can be found by multiplying the highest exponent prime factors of 19 and 24. First we will calculate the prime factors of 19 and 24.

Prime Factorization of 19


19 19
1

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

19 = 191

Prime Factorization of 24


2 24
2 12
2 6
3 3
1

Prime factors of 24 are 2,3. Prime factorization of 24 in exponential form is:

24 = 23×31

Now multiplying the highest exponent prime factors to calculate the LCM of 19 and 24.

LCM(19,24) = 23×31×191
LCM(19,24) = 456

Factors of 19

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

1, 19

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24

Least Common Multiple of 19 and 24 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 24, than apply into the LCM equation.

GCF(19,24) = 1
LCM(19,24) = ( 19 × 24) / 1
LCM(19,24) = 456 / 1
LCM(19,24) = 456

Properties of LCM 19 and 24

(i) The LCM of 24 and 19 is associative

LCM of 19 and 24 = LCM of 24 and 19

Related Least Common Multiples of 19

Related Least Common Multiples of 24

Frequently Asked Questions on LCM of 19 and 24

1. What is the LCM of 19 and 24?

Answer: LCM of 19 and 24 is 456.

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 24?

Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.

4. How to Find the LCM of 19 and 24?

Answer:

Least Common Multiple of 19 and 24 = 456

Step 1: Find the prime factorization of 19

19 = 19

Step 2: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

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

LCM = 456 = 2 x 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 19 and 24 is 456.