Least Common Multiple of 1728 and 1731

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1728 and 1731 the smallest integer that is 997056 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1731 is 997056.

LCM(1728,1731) = 997056

LCM of 1728 and 1731

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

LCM of:
and

Least Common Multiple of 1728 and 1731

LCM of 1728 and 1731 is 997056

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1731. First we will calculate the prime factors of 1728 and 1731.

Prime Factorization of 1728


2 1728
2 864
2 432
2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 1728 are 2,3. Prime factorization of 1728 in exponential form is:

1728 = 26×33

Prime Factorization of 1731


3 1731
577 577
1

Prime factors of 1731 are 3,577. Prime factorization of 1731 in exponential form is:

1731 = 31×5771

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1731.

LCM(1728,1731) = 26×33×5771
LCM(1728,1731) = 997056

Factors of 1728

List of positive integer factors of 1728 that divides 1728 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728

Factors of 1731

List of positive integer factors of 1731 that divides 1731 without a remainder.

1, 3, 577, 1731

Least Common Multiple of 1728 and 1731 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1728 and 1731, than apply into the LCM equation.

GCF(1728,1731) = 3
LCM(1728,1731) = ( 1728 × 1731) / 3
LCM(1728,1731) = 2991168 / 3
LCM(1728,1731) = 997056

Properties of LCM 1728 and 1731

(i) The LCM of 1731 and 1728 is associative

LCM of 1728 and 1731 = LCM of 1731 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1731

Frequently Asked Questions on LCM of 1728 and 1731

1. What is the LCM of 1728 and 1731?

Answer: LCM of 1728 and 1731 is 997056.

2. What are the Factors of 1728?

Answer: Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. There are 28 integers that are factors of 1728. The greatest factor of 1728 is 1728.

3. What are the Factors of 1731?

Answer: Factors of 1731 are 1, 3, 577, 1731. There are 4 integers that are factors of 1731. The greatest factor of 1731 is 1731.

4. How to Find the LCM of 1728 and 1731?

Answer:

Least Common Multiple of 1728 and 1731 = 997056

Step 1: Find the prime factorization of 1728

1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 1731

1731 = 3 x 577

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

LCM = 997056 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 577

Step 4: Therefore, the least common multiple of 1728 and 1731 is 997056.