Least Common Multiple of 720 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 720 and 728 the smallest integer that is 65520 that is divisible by both numbers.

Least Common Multiple (LCM) of 720 and 728 is 65520.

LCM(720,728) = 65520

LCM of 720 and 728

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

LCM of:
and

Least Common Multiple of 720 and 728

LCM of 720 and 728 is 65520

Least common multiple can be found by multiplying the highest exponent prime factors of 720 and 728. First we will calculate the prime factors of 720 and 728.

Prime Factorization of 720


2 720
2 360
2 180
2 90
3 45
3 15
5 5
1

Prime factors of 720 are 2, 3,5. Prime factorization of 720 in exponential form is:

720 = 24×32×51

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 720 and 728.

LCM(720,728) = 24×32×51×71×131
LCM(720,728) = 65520

Factors of 720

List of positive integer factors of 720 that divides 720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720

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 720 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 720 and 728, than apply into the LCM equation.

GCF(720,728) = 8
LCM(720,728) = ( 720 × 728) / 8
LCM(720,728) = 524160 / 8
LCM(720,728) = 65520

Properties of LCM 720 and 728

(i) The LCM of 728 and 720 is associative

LCM of 720 and 728 = LCM of 728 and 720

Related Least Common Multiples of 720

Related Least Common Multiples of 728

Frequently Asked Questions on LCM of 720 and 728

1. What is the LCM of 720 and 728?

Answer: LCM of 720 and 728 is 65520.

2. What are the Factors of 720?

Answer: Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720. There are 30 integers that are factors of 720. The greatest factor of 720 is 720.

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 720 and 728?

Answer:

Least Common Multiple of 720 and 728 = 65520

Step 1: Find the prime factorization of 720

720 = 2 x 2 x 2 x 2 x 3 x 3 x 5

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 = 65520 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 720 and 728 is 65520.