Least Common Multiple of 1728 and 1734

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 1734 the smallest integer that is 499392 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1734 is 499392.

LCM(1728,1734) = 499392

LCM of 1728 and 1734

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

LCM of:
and

Least Common Multiple of 1728 and 1734

LCM of 1728 and 1734 is 499392

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1734. First we will calculate the prime factors of 1728 and 1734.

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 1734


2 1734
3 867
17 289
17 17
1

Prime factors of 1734 are 2, 3,17. Prime factorization of 1734 in exponential form is:

1734 = 21×31×172

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1734.

LCM(1728,1734) = 26×33×172
LCM(1728,1734) = 499392

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 1734

List of positive integer factors of 1734 that divides 1734 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734

Least Common Multiple of 1728 and 1734 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 1734, than apply into the LCM equation.

GCF(1728,1734) = 6
LCM(1728,1734) = ( 1728 × 1734) / 6
LCM(1728,1734) = 2996352 / 6
LCM(1728,1734) = 499392

Properties of LCM 1728 and 1734

(i) The LCM of 1734 and 1728 is associative

LCM of 1728 and 1734 = LCM of 1734 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1734

Frequently Asked Questions on LCM of 1728 and 1734

1. What is the LCM of 1728 and 1734?

Answer: LCM of 1728 and 1734 is 499392.

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 1734?

Answer: Factors of 1734 are 1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734. There are 12 integers that are factors of 1734. The greatest factor of 1734 is 1734.

4. How to Find the LCM of 1728 and 1734?

Answer:

Least Common Multiple of 1728 and 1734 = 499392

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 1734

1734 = 2 x 3 x 17 x 17

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

LCM = 499392 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 17 x 17

Step 4: Therefore, the least common multiple of 1728 and 1734 is 499392.