Least Common Multiple of 1728 and 1735

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 1735 the smallest integer that is 2998080 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1735 is 2998080.

LCM(1728,1735) = 2998080

LCM of 1728 and 1735

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

LCM of:
and

Least Common Multiple of 1728 and 1735

LCM of 1728 and 1735 is 2998080

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1735. First we will calculate the prime factors of 1728 and 1735.

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 1735


5 1735
347 347
1

Prime factors of 1735 are 5,347. Prime factorization of 1735 in exponential form is:

1735 = 51×3471

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1735.

LCM(1728,1735) = 26×33×51×3471
LCM(1728,1735) = 2998080

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 1735

List of positive integer factors of 1735 that divides 1735 without a remainder.

1, 5, 347, 1735

Least Common Multiple of 1728 and 1735 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 1735, than apply into the LCM equation.

GCF(1728,1735) = 1
LCM(1728,1735) = ( 1728 × 1735) / 1
LCM(1728,1735) = 2998080 / 1
LCM(1728,1735) = 2998080

Properties of LCM 1728 and 1735

(i) The LCM of 1735 and 1728 is associative

LCM of 1728 and 1735 = LCM of 1735 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1735

Frequently Asked Questions on LCM of 1728 and 1735

1. What is the LCM of 1728 and 1735?

Answer: LCM of 1728 and 1735 is 2998080.

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 1735?

Answer: Factors of 1735 are 1, 5, 347, 1735. There are 4 integers that are factors of 1735. The greatest factor of 1735 is 1735.

4. How to Find the LCM of 1728 and 1735?

Answer:

Least Common Multiple of 1728 and 1735 = 2998080

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 1735

1735 = 5 x 347

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

LCM = 2998080 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 347

Step 4: Therefore, the least common multiple of 1728 and 1735 is 2998080.