Least Common Multiple of 728 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 728 and 735 the smallest integer that is 76440 that is divisible by both numbers.

Least Common Multiple (LCM) of 728 and 735 is 76440.

LCM(728,735) = 76440

LCM of 728 and 735

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

LCM of:
and

Least Common Multiple of 728 and 735

LCM of 728 and 735 is 76440

Least common multiple can be found by multiplying the highest exponent prime factors of 728 and 735. First we will calculate the prime factors of 728 and 735.

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 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 728 and 735.

LCM(728,735) = 23×31×51×72×131
LCM(728,735) = 76440

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 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 728 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 728 and 735, than apply into the LCM equation.

GCF(728,735) = 7
LCM(728,735) = ( 728 × 735) / 7
LCM(728,735) = 535080 / 7
LCM(728,735) = 76440

Properties of LCM 728 and 735

(i) The LCM of 735 and 728 is associative

LCM of 728 and 735 = LCM of 735 and 728

Related Least Common Multiples of 728

Related Least Common Multiples of 735

Frequently Asked Questions on LCM of 728 and 735

1. What is the LCM of 728 and 735?

Answer: LCM of 728 and 735 is 76440.

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 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 728 and 735?

Answer:

Least Common Multiple of 728 and 735 = 76440

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 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 = 76440 = 2 x 2 x 2 x 3 x 5 x 7 x 7 x 13

Step 4: Therefore, the least common multiple of 728 and 735 is 76440.