Least Common Multiple of 1728 and 1732

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 1732 the smallest integer that is 748224 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1732 is 748224.

LCM(1728,1732) = 748224

LCM of 1728 and 1732

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

LCM of:
and

Least Common Multiple of 1728 and 1732

LCM of 1728 and 1732 is 748224

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1732. First we will calculate the prime factors of 1728 and 1732.

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 1732


2 1732
2 866
433 433
1

Prime factors of 1732 are 2,433. Prime factorization of 1732 in exponential form is:

1732 = 22×4331

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1732.

LCM(1728,1732) = 26×33×4331
LCM(1728,1732) = 748224

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 1732

List of positive integer factors of 1732 that divides 1732 without a remainder.

1, 2, 4, 433, 866, 1732

Least Common Multiple of 1728 and 1732 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 1732, than apply into the LCM equation.

GCF(1728,1732) = 4
LCM(1728,1732) = ( 1728 × 1732) / 4
LCM(1728,1732) = 2992896 / 4
LCM(1728,1732) = 748224

Properties of LCM 1728 and 1732

(i) The LCM of 1732 and 1728 is associative

LCM of 1728 and 1732 = LCM of 1732 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1732

Frequently Asked Questions on LCM of 1728 and 1732

1. What is the LCM of 1728 and 1732?

Answer: LCM of 1728 and 1732 is 748224.

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 1732?

Answer: Factors of 1732 are 1, 2, 4, 433, 866, 1732. There are 6 integers that are factors of 1732. The greatest factor of 1732 is 1732.

4. How to Find the LCM of 1728 and 1732?

Answer:

Least Common Multiple of 1728 and 1732 = 748224

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 1732

1732 = 2 x 2 x 433

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

LCM = 748224 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 433

Step 4: Therefore, the least common multiple of 1728 and 1732 is 748224.