Least Common Multiple of 68 and 72

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 68 and 72 the smallest integer that is 1224 that is divisible by both numbers.

Least Common Multiple (LCM) of 68 and 72 is 1224.

LCM(68,72) = 1224

LCM of 68 and 72

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

LCM of:
and

Least Common Multiple of 68 and 72

LCM of 68 and 72 is 1224

Least common multiple can be found by multiplying the highest exponent prime factors of 68 and 72. First we will calculate the prime factors of 68 and 72.

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

Prime Factorization of 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

Now multiplying the highest exponent prime factors to calculate the LCM of 68 and 72.

LCM(68,72) = 23×32×171
LCM(68,72) = 1224

Factors of 68

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

1, 2, 4, 17, 34, 68

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Least Common Multiple of 68 and 72 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68 and 72, than apply into the LCM equation.

GCF(68,72) = 4
LCM(68,72) = ( 68 × 72) / 4
LCM(68,72) = 4896 / 4
LCM(68,72) = 1224

Properties of LCM 68 and 72

(i) The LCM of 72 and 68 is associative

LCM of 68 and 72 = LCM of 72 and 68

Related Least Common Multiples of 68

Related Least Common Multiples of 72

Frequently Asked Questions on LCM of 68 and 72

1. What is the LCM of 68 and 72?

Answer: LCM of 68 and 72 is 1224.

2. 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.

3. What are the Factors of 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

4. How to Find the LCM of 68 and 72?

Answer:

Least Common Multiple of 68 and 72 = 1224

Step 1: Find the prime factorization of 68

68 = 2 x 2 x 17

Step 2: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 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 = 1224 = 2 x 2 x 2 x 3 x 3 x 17

Step 4: Therefore, the least common multiple of 68 and 72 is 1224.