Least Common Multiple of 24 and 42

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 24 and 42 the smallest integer that is 168 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 42 is 168.

LCM(24,42) = 168

LCM of 24 and 42

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

LCM of:
and

Least Common Multiple of 24 and 42

LCM of 24 and 42 is 168

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 42. First we will calculate the prime factors of 24 and 42.

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

Prime Factorization of 42


2 42
3 21
7 7
1

Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:

42 = 21×31×71

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 42.

LCM(24,42) = 23×31×71
LCM(24,42) = 168

Factors of 24

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

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

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42

Least Common Multiple of 24 and 42 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 24 and 42, than apply into the LCM equation.

GCF(24,42) = 6
LCM(24,42) = ( 24 × 42) / 6
LCM(24,42) = 1008 / 6
LCM(24,42) = 168

Properties of LCM 24 and 42

(i) The LCM of 42 and 24 is associative

LCM of 24 and 42 = LCM of 42 and 24

Frequently Asked Questions on LCM of 24 and 42

1. What is the LCM of 24 and 42?

Answer: LCM of 24 and 42 is 168.

2. 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.

3. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

4. How to Find the LCM of 24 and 42?

Answer:

Least Common Multiple of 24 and 42 = 168

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 42

42 = 2 x 3 x 7

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

LCM = 168 = 2 x 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 24 and 42 is 168.