Least Common Multiple of 724 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 724 and 728 the smallest integer that is 131768 that is divisible by both numbers.

Least Common Multiple (LCM) of 724 and 728 is 131768.

LCM(724,728) = 131768

LCM of 724 and 728

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

LCM of:
and

Least Common Multiple of 724 and 728

LCM of 724 and 728 is 131768

Least common multiple can be found by multiplying the highest exponent prime factors of 724 and 728. First we will calculate the prime factors of 724 and 728.

Prime Factorization of 724


2 724
2 362
181 181
1

Prime factors of 724 are 2,181. Prime factorization of 724 in exponential form is:

724 = 22×1811

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 724 and 728.

LCM(724,728) = 23×71×131×1811
LCM(724,728) = 131768

Factors of 724

List of positive integer factors of 724 that divides 724 without a remainder.

1, 2, 4, 181, 362, 724

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 724 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 724 and 728, than apply into the LCM equation.

GCF(724,728) = 4
LCM(724,728) = ( 724 × 728) / 4
LCM(724,728) = 527072 / 4
LCM(724,728) = 131768

Properties of LCM 724 and 728

(i) The LCM of 728 and 724 is associative

LCM of 724 and 728 = LCM of 728 and 724

Related Least Common Multiples of 724

Related Least Common Multiples of 728

Frequently Asked Questions on LCM of 724 and 728

1. What is the LCM of 724 and 728?

Answer: LCM of 724 and 728 is 131768.

2. What are the Factors of 724?

Answer: Factors of 724 are 1, 2, 4, 181, 362, 724. There are 6 integers that are factors of 724. The greatest factor of 724 is 724.

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 724 and 728?

Answer:

Least Common Multiple of 724 and 728 = 131768

Step 1: Find the prime factorization of 724

724 = 2 x 2 x 181

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 = 131768 = 2 x 2 x 2 x 7 x 13 x 181

Step 4: Therefore, the least common multiple of 724 and 728 is 131768.