Least Common Multiple of 728 and 729

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 728 and 729 the smallest integer that is 530712 that is divisible by both numbers.

Least Common Multiple (LCM) of 728 and 729 is 530712.

LCM(728,729) = 530712

LCM of 728 and 729

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

LCM of:
and

Least Common Multiple of 728 and 729

LCM of 728 and 729 is 530712

Least common multiple can be found by multiplying the highest exponent prime factors of 728 and 729. First we will calculate the prime factors of 728 and 729.

Prime Factorization of 728


2 728
2 364
2 182
7 91
13 13
1

Prime factors of 728 are 2, 7,13. Prime factorization of 728 in exponential form is:

728 = 23×71×131

Prime Factorization of 729


3 729
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 729 are 3. Prime factorization of 729 in exponential form is:

729 = 36

Now multiplying the highest exponent prime factors to calculate the LCM of 728 and 729.

LCM(728,729) = 23×36×71×131
LCM(728,729) = 530712

Factors of 728

List of positive integer factors of 728 that divides 728 without a remainder.

1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

Factors of 729

List of positive integer factors of 729 that divides 729 without a remainder.

1, 3, 9, 27, 81, 243, 729

Least Common Multiple of 728 and 729 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 728 and 729, than apply into the LCM equation.

GCF(728,729) = 1
LCM(728,729) = ( 728 × 729) / 1
LCM(728,729) = 530712 / 1
LCM(728,729) = 530712

Properties of LCM 728 and 729

(i) The LCM of 729 and 728 is associative

LCM of 728 and 729 = LCM of 729 and 728

Related Least Common Multiples of 728

Related Least Common Multiples of 729

Frequently Asked Questions on LCM of 728 and 729

1. What is the LCM of 728 and 729?

Answer: LCM of 728 and 729 is 530712.

2. What are the Factors of 728?

Answer: Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. There are 16 integers that are factors of 728. The greatest factor of 728 is 728.

3. What are the Factors of 729?

Answer: Factors of 729 are 1, 3, 9, 27, 81, 243, 729. There are 7 integers that are factors of 729. The greatest factor of 729 is 729.

4. How to Find the LCM of 728 and 729?

Answer:

Least Common Multiple of 728 and 729 = 530712

Step 1: Find the prime factorization of 728

728 = 2 x 2 x 2 x 7 x 13

Step 2: Find the prime factorization of 729

729 = 3 x 3 x 3 x 3 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 = 530712 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 7 x 13

Step 4: Therefore, the least common multiple of 728 and 729 is 530712.