Least Common Multiple of 1728 and 1736

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 1736 the smallest integer that is 374976 that is divisible by both numbers.

Least Common Multiple (LCM) of 1728 and 1736 is 374976.

LCM(1728,1736) = 374976

LCM of 1728 and 1736

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

LCM of:
and

Least Common Multiple of 1728 and 1736

LCM of 1728 and 1736 is 374976

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1736. First we will calculate the prime factors of 1728 and 1736.

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 1736


2 1736
2 868
2 434
7 217
31 31
1

Prime factors of 1736 are 2, 7,31. Prime factorization of 1736 in exponential form is:

1736 = 23×71×311

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1736.

LCM(1728,1736) = 26×33×71×311
LCM(1728,1736) = 374976

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 1736

List of positive integer factors of 1736 that divides 1736 without a remainder.

1, 2, 4, 7, 8, 14, 28, 31, 56, 62, 124, 217, 248, 434, 868, 1736

Least Common Multiple of 1728 and 1736 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 1736, than apply into the LCM equation.

GCF(1728,1736) = 8
LCM(1728,1736) = ( 1728 × 1736) / 8
LCM(1728,1736) = 2999808 / 8
LCM(1728,1736) = 374976

Properties of LCM 1728 and 1736

(i) The LCM of 1736 and 1728 is associative

LCM of 1728 and 1736 = LCM of 1736 and 1728

Related Least Common Multiples of 1728

Related Least Common Multiples of 1736

Frequently Asked Questions on LCM of 1728 and 1736

1. What is the LCM of 1728 and 1736?

Answer: LCM of 1728 and 1736 is 374976.

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 1736?

Answer: Factors of 1736 are 1, 2, 4, 7, 8, 14, 28, 31, 56, 62, 124, 217, 248, 434, 868, 1736. There are 16 integers that are factors of 1736. The greatest factor of 1736 is 1736.

4. How to Find the LCM of 1728 and 1736?

Answer:

Least Common Multiple of 1728 and 1736 = 374976

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 1736

1736 = 2 x 2 x 2 x 7 x 31

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

LCM = 374976 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 31

Step 4: Therefore, the least common multiple of 1728 and 1736 is 374976.