Least Common Multiple of 723 and 726

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 726 the smallest integer that is 174966 that is divisible by both numbers.

Least Common Multiple (LCM) of 723 and 726 is 174966.

LCM(723,726) = 174966

LCM of 723 and 726

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

LCM of:
and

Least Common Multiple of 723 and 726

LCM of 723 and 726 is 174966

Least common multiple can be found by multiplying the highest exponent prime factors of 723 and 726. First we will calculate the prime factors of 723 and 726.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 723 and 726.

LCM(723,726) = 21×31×112×2411
LCM(723,726) = 174966

Factors of 723

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

1, 3, 241, 723

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

Least Common Multiple of 723 and 726 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 726, than apply into the LCM equation.

GCF(723,726) = 3
LCM(723,726) = ( 723 × 726) / 3
LCM(723,726) = 524898 / 3
LCM(723,726) = 174966

Properties of LCM 723 and 726

(i) The LCM of 726 and 723 is associative

LCM of 723 and 726 = LCM of 726 and 723

Related Least Common Multiples of 723

Related Least Common Multiples of 726

Frequently Asked Questions on LCM of 723 and 726

1. What is the LCM of 723 and 726?

Answer: LCM of 723 and 726 is 174966.

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 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.

4. How to Find the LCM of 723 and 726?

Answer:

Least Common Multiple of 723 and 726 = 174966

Step 1: Find the prime factorization of 723

723 = 3 x 241

Step 2: Find the prime factorization of 726

726 = 2 x 3 x 11 x 11

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

LCM = 174966 = 2 x 3 x 11 x 11 x 241

Step 4: Therefore, the least common multiple of 723 and 726 is 174966.