Least Common Multiple of 1800 and 1804

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1800 and 1804 the smallest integer that is 811800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1800 and 1804 is 811800.

LCM(1800,1804) = 811800

LCM of 1800 and 1804

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

LCM of:
and

Least Common Multiple of 1800 and 1804

LCM of 1800 and 1804 is 811800

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1804. First we will calculate the prime factors of 1800 and 1804.

Prime Factorization of 1800


2 1800
2 900
2 450
3 225
3 75
5 25
5 5
1

Prime factors of 1800 are 2, 3,5. Prime factorization of 1800 in exponential form is:

1800 = 23×32×52

Prime Factorization of 1804


2 1804
2 902
11 451
41 41
1

Prime factors of 1804 are 2, 11,41. Prime factorization of 1804 in exponential form is:

1804 = 22×111×411

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1804.

LCM(1800,1804) = 23×32×52×111×411
LCM(1800,1804) = 811800

Factors of 1800

List of positive integer factors of 1800 that divides 1800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800

Factors of 1804

List of positive integer factors of 1804 that divides 1804 without a remainder.

1, 2, 4, 11, 22, 41, 44, 82, 164, 451, 902, 1804

Least Common Multiple of 1800 and 1804 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1800 and 1804, than apply into the LCM equation.

GCF(1800,1804) = 4
LCM(1800,1804) = ( 1800 × 1804) / 4
LCM(1800,1804) = 3247200 / 4
LCM(1800,1804) = 811800

Properties of LCM 1800 and 1804

(i) The LCM of 1804 and 1800 is associative

LCM of 1800 and 1804 = LCM of 1804 and 1800

Related Least Common Multiples of 1800

Related Least Common Multiples of 1804

Frequently Asked Questions on LCM of 1800 and 1804

1. What is the LCM of 1800 and 1804?

Answer: LCM of 1800 and 1804 is 811800.

2. What are the Factors of 1800?

Answer: Factors of 1800 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800. There are 36 integers that are factors of 1800. The greatest factor of 1800 is 1800.

3. What are the Factors of 1804?

Answer: Factors of 1804 are 1, 2, 4, 11, 22, 41, 44, 82, 164, 451, 902, 1804. There are 12 integers that are factors of 1804. The greatest factor of 1804 is 1804.

4. How to Find the LCM of 1800 and 1804?

Answer:

Least Common Multiple of 1800 and 1804 = 811800

Step 1: Find the prime factorization of 1800

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 1804

1804 = 2 x 2 x 11 x 41

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

LCM = 811800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 11 x 41

Step 4: Therefore, the least common multiple of 1800 and 1804 is 811800.