Least Common Multiple of 726 and 728

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 726 and 728 the smallest integer that is 264264 that is divisible by both numbers.

Least Common Multiple (LCM) of 726 and 728 is 264264.

LCM(726,728) = 264264

LCM of 726 and 728

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

LCM of:
and

Least Common Multiple of 726 and 728

LCM of 726 and 728 is 264264

Least common multiple can be found by multiplying the highest exponent prime factors of 726 and 728. First we will calculate the prime factors of 726 and 728.

Prime Factorization of 726


2 726
3 363
11 121
11 11
1

Prime factors of 726 are 2, 3,11. Prime factorization of 726 in exponential form is:

726 = 21×31×112

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

Now multiplying the highest exponent prime factors to calculate the LCM of 726 and 728.

LCM(726,728) = 23×31×71×112×131
LCM(726,728) = 264264

Factors of 726

List of positive integer factors of 726 that divides 726 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726

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

Least Common Multiple of 726 and 728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 726 and 728, than apply into the LCM equation.

GCF(726,728) = 2
LCM(726,728) = ( 726 × 728) / 2
LCM(726,728) = 528528 / 2
LCM(726,728) = 264264

Properties of LCM 726 and 728

(i) The LCM of 728 and 726 is associative

LCM of 726 and 728 = LCM of 728 and 726

Related Least Common Multiples of 726

Related Least Common Multiples of 728

Frequently Asked Questions on LCM of 726 and 728

1. What is the LCM of 726 and 728?

Answer: LCM of 726 and 728 is 264264.

2. What are the Factors of 726?

Answer: Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726. There are 12 integers that are factors of 726. The greatest factor of 726 is 726.

3. 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.

4. How to Find the LCM of 726 and 728?

Answer:

Least Common Multiple of 726 and 728 = 264264

Step 1: Find the prime factorization of 726

726 = 2 x 3 x 11 x 11

Step 2: Find the prime factorization of 728

728 = 2 x 2 x 2 x 7 x 13

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 264264 = 2 x 2 x 2 x 3 x 7 x 11 x 11 x 13

Step 4: Therefore, the least common multiple of 726 and 728 is 264264.