Least Common Multiple of 1728 and 1729

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 1729 the smallest integer that is 2987712 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1729 is 2987712.

LCM(1728,1729) = 2987712

LCM of 1728 and 1729

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

LCM of:
and

Least Common Multiple of 1728 and 1729

LCM of 1728 and 1729 is 2987712

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1729. First we will calculate the prime factors of 1728 and 1729.

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 1729


7 1729
13 247
19 19
1

Prime factors of 1729 are 7, 13,19. Prime factorization of 1729 in exponential form is:

1729 = 71×131×191

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1729.

LCM(1728,1729) = 26×33×71×131×191
LCM(1728,1729) = 2987712

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 1729

List of positive integer factors of 1729 that divides 1729 without a remainder.

1, 7, 13, 19, 91, 133, 247, 1729

Least Common Multiple of 1728 and 1729 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 1729, than apply into the LCM equation.

GCF(1728,1729) = 1
LCM(1728,1729) = ( 1728 × 1729) / 1
LCM(1728,1729) = 2987712 / 1
LCM(1728,1729) = 2987712

Properties of LCM 1728 and 1729

(i) The LCM of 1729 and 1728 is associative

LCM of 1728 and 1729 = LCM of 1729 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1729

Frequently Asked Questions on LCM of 1728 and 1729

1. What is the LCM of 1728 and 1729?

Answer: LCM of 1728 and 1729 is 2987712.

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 1729?

Answer: Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729. There are 8 integers that are factors of 1729. The greatest factor of 1729 is 1729.

4. How to Find the LCM of 1728 and 1729?

Answer:

Least Common Multiple of 1728 and 1729 = 2987712

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 1729

1729 = 7 x 13 x 19

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

LCM = 2987712 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 13 x 19

Step 4: Therefore, the least common multiple of 1728 and 1729 is 2987712.