Least Common Multiple of 1800 and 1803

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 1803 the smallest integer that is 1081800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1800 and 1803 is 1081800.

LCM(1800,1803) = 1081800

LCM of 1800 and 1803

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

LCM of:
and

Least Common Multiple of 1800 and 1803

LCM of 1800 and 1803 is 1081800

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1803. First we will calculate the prime factors of 1800 and 1803.

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 1803


3 1803
601 601
1

Prime factors of 1803 are 3,601. Prime factorization of 1803 in exponential form is:

1803 = 31×6011

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1803.

LCM(1800,1803) = 23×32×52×6011
LCM(1800,1803) = 1081800

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 1803

List of positive integer factors of 1803 that divides 1803 without a remainder.

1, 3, 601, 1803

Least Common Multiple of 1800 and 1803 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 1803, than apply into the LCM equation.

GCF(1800,1803) = 3
LCM(1800,1803) = ( 1800 × 1803) / 3
LCM(1800,1803) = 3245400 / 3
LCM(1800,1803) = 1081800

Properties of LCM 1800 and 1803

(i) The LCM of 1803 and 1800 is associative

LCM of 1800 and 1803 = LCM of 1803 and 1800

Related Least Common Multiples of 1800

Related Least Common Multiples of 1803

Frequently Asked Questions on LCM of 1800 and 1803

1. What is the LCM of 1800 and 1803?

Answer: LCM of 1800 and 1803 is 1081800.

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 1803?

Answer: Factors of 1803 are 1, 3, 601, 1803. There are 4 integers that are factors of 1803. The greatest factor of 1803 is 1803.

4. How to Find the LCM of 1800 and 1803?

Answer:

Least Common Multiple of 1800 and 1803 = 1081800

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 1803

1803 = 3 x 601

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

LCM = 1081800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 601

Step 4: Therefore, the least common multiple of 1800 and 1803 is 1081800.