Least Common Multiple of 1800 and 1806

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 1806 the smallest integer that is 541800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1800 and 1806 is 541800.

LCM(1800,1806) = 541800

LCM of 1800 and 1806

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

LCM of:
and

Least Common Multiple of 1800 and 1806

LCM of 1800 and 1806 is 541800

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1806. First we will calculate the prime factors of 1800 and 1806.

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 1806


2 1806
3 903
7 301
43 43
1

Prime factors of 1806 are 2, 3, 7,43. Prime factorization of 1806 in exponential form is:

1806 = 21×31×71×431

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1806.

LCM(1800,1806) = 23×32×52×71×431
LCM(1800,1806) = 541800

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 1806

List of positive integer factors of 1806 that divides 1806 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903, 1806

Least Common Multiple of 1800 and 1806 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 1806, than apply into the LCM equation.

GCF(1800,1806) = 6
LCM(1800,1806) = ( 1800 × 1806) / 6
LCM(1800,1806) = 3250800 / 6
LCM(1800,1806) = 541800

Properties of LCM 1800 and 1806

(i) The LCM of 1806 and 1800 is associative

LCM of 1800 and 1806 = LCM of 1806 and 1800

Related Least Common Multiples of 1800

Related Least Common Multiples of 1806

Frequently Asked Questions on LCM of 1800 and 1806

1. What is the LCM of 1800 and 1806?

Answer: LCM of 1800 and 1806 is 541800.

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 1806?

Answer: Factors of 1806 are 1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903, 1806. There are 16 integers that are factors of 1806. The greatest factor of 1806 is 1806.

4. How to Find the LCM of 1800 and 1806?

Answer:

Least Common Multiple of 1800 and 1806 = 541800

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 1806

1806 = 2 x 3 x 7 x 43

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

LCM = 541800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 43

Step 4: Therefore, the least common multiple of 1800 and 1806 is 541800.