Least Common Multiple of 720 and 723

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 723 the smallest integer that is 173520 that is divisible by both numbers.

Least Common Multiple (LCM) of 720 and 723 is 173520.

LCM(720,723) = 173520

LCM of 720 and 723

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

LCM of:
and

Least Common Multiple of 720 and 723

LCM of 720 and 723 is 173520

Least common multiple can be found by multiplying the highest exponent prime factors of 720 and 723. First we will calculate the prime factors of 720 and 723.

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 723


3 723
241 241
1

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

723 = 31×2411

Now multiplying the highest exponent prime factors to calculate the LCM of 720 and 723.

LCM(720,723) = 24×32×51×2411
LCM(720,723) = 173520

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 723

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

1, 3, 241, 723

Least Common Multiple of 720 and 723 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 723, than apply into the LCM equation.

GCF(720,723) = 3
LCM(720,723) = ( 720 × 723) / 3
LCM(720,723) = 520560 / 3
LCM(720,723) = 173520

Properties of LCM 720 and 723

(i) The LCM of 723 and 720 is associative

LCM of 720 and 723 = LCM of 723 and 720

Related Least Common Multiples of 720

Related Least Common Multiples of 723

Frequently Asked Questions on LCM of 720 and 723

1. What is the LCM of 720 and 723?

Answer: LCM of 720 and 723 is 173520.

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 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.

4. How to Find the LCM of 720 and 723?

Answer:

Least Common Multiple of 720 and 723 = 173520

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 723

723 = 3 x 241

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

LCM = 173520 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 241

Step 4: Therefore, the least common multiple of 720 and 723 is 173520.