Least Common Multiple of 722 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 722 and 728 the smallest integer that is 262808 that is divisible by both numbers.

Least Common Multiple (LCM) of 722 and 728 is 262808.

LCM(722,728) = 262808

LCM of 722 and 728

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

LCM of:
and

Least Common Multiple of 722 and 728

LCM of 722 and 728 is 262808

Least common multiple can be found by multiplying the highest exponent prime factors of 722 and 728. First we will calculate the prime factors of 722 and 728.

Prime Factorization of 722


2 722
19 361
19 19
1

Prime factors of 722 are 2,19. Prime factorization of 722 in exponential form is:

722 = 21×192

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 722 and 728.

LCM(722,728) = 23×71×131×192
LCM(722,728) = 262808

Factors of 722

List of positive integer factors of 722 that divides 722 without a remainder.

1, 2, 19, 38, 361, 722

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 722 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 722 and 728, than apply into the LCM equation.

GCF(722,728) = 2
LCM(722,728) = ( 722 × 728) / 2
LCM(722,728) = 525616 / 2
LCM(722,728) = 262808

Properties of LCM 722 and 728

(i) The LCM of 728 and 722 is associative

LCM of 722 and 728 = LCM of 728 and 722

Related Least Common Multiples of 722

Related Least Common Multiples of 728

Frequently Asked Questions on LCM of 722 and 728

1. What is the LCM of 722 and 728?

Answer: LCM of 722 and 728 is 262808.

2. What are the Factors of 722?

Answer: Factors of 722 are 1, 2, 19, 38, 361, 722. There are 6 integers that are factors of 722. The greatest factor of 722 is 722.

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 722 and 728?

Answer:

Least Common Multiple of 722 and 728 = 262808

Step 1: Find the prime factorization of 722

722 = 2 x 19 x 19

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 = 262808 = 2 x 2 x 2 x 7 x 13 x 19 x 19

Step 4: Therefore, the least common multiple of 722 and 728 is 262808.