Least Common Multiple of 729 and 735

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 729 and 735 the smallest integer that is 178605 that is divisible by both numbers.

Least Common Multiple (LCM) of 729 and 735 is 178605.

LCM(729,735) = 178605

LCM of 729 and 735

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

LCM of:
and

Least Common Multiple of 729 and 735

LCM of 729 and 735 is 178605

Least common multiple can be found by multiplying the highest exponent prime factors of 729 and 735. First we will calculate the prime factors of 729 and 735.

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

Prime Factorization of 735


3 735
5 245
7 49
7 7
1

Prime factors of 735 are 3, 5,7. Prime factorization of 735 in exponential form is:

735 = 31×51×72

Now multiplying the highest exponent prime factors to calculate the LCM of 729 and 735.

LCM(729,735) = 36×51×72
LCM(729,735) = 178605

Factors of 729

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

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

Factors of 735

List of positive integer factors of 735 that divides 735 without a remainder.

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735

Least Common Multiple of 729 and 735 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 729 and 735, than apply into the LCM equation.

GCF(729,735) = 3
LCM(729,735) = ( 729 × 735) / 3
LCM(729,735) = 535815 / 3
LCM(729,735) = 178605

Properties of LCM 729 and 735

(i) The LCM of 735 and 729 is associative

LCM of 729 and 735 = LCM of 735 and 729

Related Least Common Multiples of 729

Related Least Common Multiples of 735

Frequently Asked Questions on LCM of 729 and 735

1. What is the LCM of 729 and 735?

Answer: LCM of 729 and 735 is 178605.

2. 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.

3. What are the Factors of 735?

Answer: Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. There are 12 integers that are factors of 735. The greatest factor of 735 is 735.

4. How to Find the LCM of 729 and 735?

Answer:

Least Common Multiple of 729 and 735 = 178605

Step 1: Find the prime factorization of 729

729 = 3 x 3 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 735

735 = 3 x 5 x 7 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 = 178605 = 3 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 7

Step 4: Therefore, the least common multiple of 729 and 735 is 178605.