Least Common Multiple of 1728 and 1730

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 1730 the smallest integer that is 1494720 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1730 is 1494720.

LCM(1728,1730) = 1494720

LCM of 1728 and 1730

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

LCM of:
and

Least Common Multiple of 1728 and 1730

LCM of 1728 and 1730 is 1494720

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1730. First we will calculate the prime factors of 1728 and 1730.

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 1730


2 1730
5 865
173 173
1

Prime factors of 1730 are 2, 5,173. Prime factorization of 1730 in exponential form is:

1730 = 21×51×1731

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1730.

LCM(1728,1730) = 26×33×51×1731
LCM(1728,1730) = 1494720

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 1730

List of positive integer factors of 1730 that divides 1730 without a remainder.

1, 2, 5, 10, 173, 346, 865, 1730

Least Common Multiple of 1728 and 1730 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 1730, than apply into the LCM equation.

GCF(1728,1730) = 2
LCM(1728,1730) = ( 1728 × 1730) / 2
LCM(1728,1730) = 2989440 / 2
LCM(1728,1730) = 1494720

Properties of LCM 1728 and 1730

(i) The LCM of 1730 and 1728 is associative

LCM of 1728 and 1730 = LCM of 1730 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1730

Frequently Asked Questions on LCM of 1728 and 1730

1. What is the LCM of 1728 and 1730?

Answer: LCM of 1728 and 1730 is 1494720.

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 1730?

Answer: Factors of 1730 are 1, 2, 5, 10, 173, 346, 865, 1730. There are 8 integers that are factors of 1730. The greatest factor of 1730 is 1730.

4. How to Find the LCM of 1728 and 1730?

Answer:

Least Common Multiple of 1728 and 1730 = 1494720

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 1730

1730 = 2 x 5 x 173

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

LCM = 1494720 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 173

Step 4: Therefore, the least common multiple of 1728 and 1730 is 1494720.