Least Common Multiple of 723 and 724

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 723 and 724 the smallest integer that is 523452 that is divisible by both numbers.

Least Common Multiple (LCM) of 723 and 724 is 523452.

LCM(723,724) = 523452

LCM of 723 and 724

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

LCM of:
and

Least Common Multiple of 723 and 724

LCM of 723 and 724 is 523452

Least common multiple can be found by multiplying the highest exponent prime factors of 723 and 724. First we will calculate the prime factors of 723 and 724.

Prime Factorization of 723


3 723
241 241
1

Prime factors of 723 are 3,241. Prime factorization of 723 in exponential form is:

723 = 31×2411

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

Now multiplying the highest exponent prime factors to calculate the LCM of 723 and 724.

LCM(723,724) = 22×31×1811×2411
LCM(723,724) = 523452

Factors of 723

List of positive integer factors of 723 that divides 723 without a remainder.

1, 3, 241, 723

Factors of 724

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

1, 2, 4, 181, 362, 724

Least Common Multiple of 723 and 724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 723 and 724, than apply into the LCM equation.

GCF(723,724) = 1
LCM(723,724) = ( 723 × 724) / 1
LCM(723,724) = 523452 / 1
LCM(723,724) = 523452

Properties of LCM 723 and 724

(i) The LCM of 724 and 723 is associative

LCM of 723 and 724 = LCM of 724 and 723

Related Least Common Multiples of 723

Related Least Common Multiples of 724

Frequently Asked Questions on LCM of 723 and 724

1. What is the LCM of 723 and 724?

Answer: LCM of 723 and 724 is 523452.

2. What are the Factors of 723?

Answer: Factors of 723 are 1, 3, 241, 723. There are 4 integers that are factors of 723. The greatest factor of 723 is 723.

3. 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.

4. How to Find the LCM of 723 and 724?

Answer:

Least Common Multiple of 723 and 724 = 523452

Step 1: Find the prime factorization of 723

723 = 3 x 241

Step 2: Find the prime factorization of 724

724 = 2 x 2 x 181

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

LCM = 523452 = 2 x 2 x 3 x 181 x 241

Step 4: Therefore, the least common multiple of 723 and 724 is 523452.