Least Common Multiple of 1728 and 1733

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 1733 the smallest integer that is 2994624 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1733 is 2994624.

LCM(1728,1733) = 2994624

LCM of 1728 and 1733

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

LCM of:
and

Least Common Multiple of 1728 and 1733

LCM of 1728 and 1733 is 2994624

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1733. First we will calculate the prime factors of 1728 and 1733.

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 1733


1733 1733
1

Prime factors of 1733 are 1733. Prime factorization of 1733 in exponential form is:

1733 = 17331

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1733.

LCM(1728,1733) = 26×33×17331
LCM(1728,1733) = 2994624

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 1733

List of positive integer factors of 1733 that divides 1733 without a remainder.

1, 1733

Least Common Multiple of 1728 and 1733 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 1733, than apply into the LCM equation.

GCF(1728,1733) = 1
LCM(1728,1733) = ( 1728 × 1733) / 1
LCM(1728,1733) = 2994624 / 1
LCM(1728,1733) = 2994624

Properties of LCM 1728 and 1733

(i) The LCM of 1733 and 1728 is associative

LCM of 1728 and 1733 = LCM of 1733 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1733

Frequently Asked Questions on LCM of 1728 and 1733

1. What is the LCM of 1728 and 1733?

Answer: LCM of 1728 and 1733 is 2994624.

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 1733?

Answer: Factors of 1733 are 1, 1733. There are 2 integers that are factors of 1733. The greatest factor of 1733 is 1733.

4. How to Find the LCM of 1728 and 1733?

Answer:

Least Common Multiple of 1728 and 1733 = 2994624

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 1733

1733 = 1733

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

LCM = 2994624 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1733

Step 4: Therefore, the least common multiple of 1728 and 1733 is 2994624.