Least Common Multiple of 1723 and 1728

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1723 and 1728 the smallest integer that is 2977344 that is divisible by both numbers.

Least Common Multiple (LCM) of 1723 and 1728 is 2977344.

LCM(1723,1728) = 2977344

LCM of 1723 and 1728

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

LCM of:
and

Least Common Multiple of 1723 and 1728

LCM of 1723 and 1728 is 2977344

Least common multiple can be found by multiplying the highest exponent prime factors of 1723 and 1728. First we will calculate the prime factors of 1723 and 1728.

Prime Factorization of 1723


1723 1723
1

Prime factors of 1723 are 1723. Prime factorization of 1723 in exponential form is:

1723 = 17231

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1723 and 1728.

LCM(1723,1728) = 26×33×17231
LCM(1723,1728) = 2977344

Factors of 1723

List of positive integer factors of 1723 that divides 1723 without a remainder.

1, 1723

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

Least Common Multiple of 1723 and 1728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1723 and 1728, than apply into the LCM equation.

GCF(1723,1728) = 1
LCM(1723,1728) = ( 1723 × 1728) / 1
LCM(1723,1728) = 2977344 / 1
LCM(1723,1728) = 2977344

Properties of LCM 1723 and 1728

(i) The LCM of 1728 and 1723 is associative

LCM of 1723 and 1728 = LCM of 1728 and 1723

Related Least Common Multiples of 1723

Related Least Common Multiples of 1728

Frequently Asked Questions on LCM of 1723 and 1728

1. What is the LCM of 1723 and 1728?

Answer: LCM of 1723 and 1728 is 2977344.

2. What are the Factors of 1723?

Answer: Factors of 1723 are 1, 1723. There are 2 integers that are factors of 1723. The greatest factor of 1723 is 1723.

3. 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.

4. How to Find the LCM of 1723 and 1728?

Answer:

Least Common Multiple of 1723 and 1728 = 2977344

Step 1: Find the prime factorization of 1723

1723 = 1723

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2977344 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1723

Step 4: Therefore, the least common multiple of 1723 and 1728 is 2977344.