Least Common Multiple of 1722 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 1722 and 1728 the smallest integer that is 495936 that is divisible by both numbers.

Least Common Multiple (LCM) of 1722 and 1728 is 495936.

LCM(1722,1728) = 495936

LCM of 1722 and 1728

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

LCM of:
and

Least Common Multiple of 1722 and 1728

LCM of 1722 and 1728 is 495936

Least common multiple can be found by multiplying the highest exponent prime factors of 1722 and 1728. First we will calculate the prime factors of 1722 and 1728.

Prime Factorization of 1722


2 1722
3 861
7 287
41 41
1

Prime factors of 1722 are 2, 3, 7,41. Prime factorization of 1722 in exponential form is:

1722 = 21×31×71×411

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 1722 and 1728.

LCM(1722,1728) = 26×33×71×411
LCM(1722,1728) = 495936

Factors of 1722

List of positive integer factors of 1722 that divides 1722 without a remainder.

1, 2, 3, 6, 7, 14, 21, 41, 42, 82, 123, 246, 287, 574, 861, 1722

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 1722 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 1722 and 1728, than apply into the LCM equation.

GCF(1722,1728) = 6
LCM(1722,1728) = ( 1722 × 1728) / 6
LCM(1722,1728) = 2975616 / 6
LCM(1722,1728) = 495936

Properties of LCM 1722 and 1728

(i) The LCM of 1728 and 1722 is associative

LCM of 1722 and 1728 = LCM of 1728 and 1722

Related Least Common Multiples of 1722

Related Least Common Multiples of 1728

Frequently Asked Questions on LCM of 1722 and 1728

1. What is the LCM of 1722 and 1728?

Answer: LCM of 1722 and 1728 is 495936.

2. What are the Factors of 1722?

Answer: Factors of 1722 are 1, 2, 3, 6, 7, 14, 21, 41, 42, 82, 123, 246, 287, 574, 861, 1722. There are 16 integers that are factors of 1722. The greatest factor of 1722 is 1722.

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 1722 and 1728?

Answer:

Least Common Multiple of 1722 and 1728 = 495936

Step 1: Find the prime factorization of 1722

1722 = 2 x 3 x 7 x 41

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 = 495936 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 41

Step 4: Therefore, the least common multiple of 1722 and 1728 is 495936.