Least Common Multiple of 1724 and 1728

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1724 and 1728 the smallest integer that is 744768 that is divisible by both numbers.

Least Common Multiple (LCM) of 1724 and 1728 is 744768.

LCM(1724,1728) = 744768

LCM of 1724 and 1728

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

LCM of:
and

Least Common Multiple of 1724 and 1728

LCM of 1724 and 1728 is 744768

Least common multiple can be found by multiplying the highest exponent prime factors of 1724 and 1728. First we will calculate the prime factors of 1724 and 1728.

Prime Factorization of 1724


2 1724
2 862
431 431
1

Prime factors of 1724 are 2,431. Prime factorization of 1724 in exponential form is:

1724 = 22×4311

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1724 and 1728.

LCM(1724,1728) = 26×33×4311
LCM(1724,1728) = 744768

Factors of 1724

List of positive integer factors of 1724 that divides 1724 without a remainder.

1, 2, 4, 431, 862, 1724

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

Least Common Multiple of 1724 and 1728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1724 and 1728, than apply into the LCM equation.

GCF(1724,1728) = 4
LCM(1724,1728) = ( 1724 × 1728) / 4
LCM(1724,1728) = 2979072 / 4
LCM(1724,1728) = 744768

Properties of LCM 1724 and 1728

(i) The LCM of 1728 and 1724 is associative

LCM of 1724 and 1728 = LCM of 1728 and 1724

Related Least Common Multiples of 1724

Related Least Common Multiples of 1728

Frequently Asked Questions on LCM of 1724 and 1728

1. What is the LCM of 1724 and 1728?

Answer: LCM of 1724 and 1728 is 744768.

2. What are the Factors of 1724?

Answer: Factors of 1724 are 1, 2, 4, 431, 862, 1724. There are 6 integers that are factors of 1724. The greatest factor of 1724 is 1724.

3. 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.

4. How to Find the LCM of 1724 and 1728?

Answer:

Least Common Multiple of 1724 and 1728 = 744768

Step 1: Find the prime factorization of 1724

1724 = 2 x 2 x 431

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 744768 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 431

Step 4: Therefore, the least common multiple of 1724 and 1728 is 744768.