Least Common Multiple of 24 and 68

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 68 the smallest integer that is 408 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 68 is 408.

LCM(24,68) = 408

LCM of 24 and 68

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

LCM of:
and

Least Common Multiple of 24 and 68

LCM of 24 and 68 is 408

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 68. First we will calculate the prime factors of 24 and 68.

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 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 68.

LCM(24,68) = 23×31×171
LCM(24,68) = 408

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 68

List of positive integer factors of 68 that divides 68 without a remainder.

1, 2, 4, 17, 34, 68

Least Common Multiple of 24 and 68 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 68, than apply into the LCM equation.

GCF(24,68) = 4
LCM(24,68) = ( 24 × 68) / 4
LCM(24,68) = 1632 / 4
LCM(24,68) = 408

Properties of LCM 24 and 68

(i) The LCM of 68 and 24 is associative

LCM of 24 and 68 = LCM of 68 and 24

Related Least Common Multiples of 24

Related Least Common Multiples of 68

Frequently Asked Questions on LCM of 24 and 68

1. What is the LCM of 24 and 68?

Answer: LCM of 24 and 68 is 408.

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 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

4. How to Find the LCM of 24 and 68?

Answer:

Least Common Multiple of 24 and 68 = 408

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 68

68 = 2 x 2 x 17

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

LCM = 408 = 2 x 2 x 2 x 3 x 17

Step 4: Therefore, the least common multiple of 24 and 68 is 408.