Least Common Multiple of 723 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 723 and 729 the smallest integer that is 175689 that is divisible by both numbers.

Least Common Multiple (LCM) of 723 and 729 is 175689.

LCM(723,729) = 175689

LCM of 723 and 729

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

LCM of:
and

Least Common Multiple of 723 and 729

LCM of 723 and 729 is 175689

Least common multiple can be found by multiplying the highest exponent prime factors of 723 and 729. First we will calculate the prime factors of 723 and 729.

Prime Factorization of 723


3 723
241 241
1

Prime factors of 723 are 3,241. Prime factorization of 723 in exponential form is:

723 = 31×2411

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 723 and 729.

LCM(723,729) = 36×2411
LCM(723,729) = 175689

Factors of 723

List of positive integer factors of 723 that divides 723 without a remainder.

1, 3, 241, 723

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 723 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 723 and 729, than apply into the LCM equation.

GCF(723,729) = 3
LCM(723,729) = ( 723 × 729) / 3
LCM(723,729) = 527067 / 3
LCM(723,729) = 175689

Properties of LCM 723 and 729

(i) The LCM of 729 and 723 is associative

LCM of 723 and 729 = LCM of 729 and 723

Related Least Common Multiples of 723

Related Least Common Multiples of 729

Frequently Asked Questions on LCM of 723 and 729

1. What is the LCM of 723 and 729?

Answer: LCM of 723 and 729 is 175689.

2. What are the Factors of 723?

Answer: Factors of 723 are 1, 3, 241, 723. There are 4 integers that are factors of 723. The greatest factor of 723 is 723.

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 723 and 729?

Answer:

Least Common Multiple of 723 and 729 = 175689

Step 1: Find the prime factorization of 723

723 = 3 x 241

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 = 175689 = 3 x 3 x 3 x 3 x 3 x 3 x 241

Step 4: Therefore, the least common multiple of 723 and 729 is 175689.