Least Common Multiple of 1800 and 1805

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 1805 the smallest integer that is 649800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1800 and 1805 is 649800.

LCM(1800,1805) = 649800

LCM of 1800 and 1805

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

LCM of:
and

Least Common Multiple of 1800 and 1805

LCM of 1800 and 1805 is 649800

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1805. First we will calculate the prime factors of 1800 and 1805.

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 1805


5 1805
19 361
19 19
1

Prime factors of 1805 are 5,19. Prime factorization of 1805 in exponential form is:

1805 = 51×192

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1805.

LCM(1800,1805) = 23×32×52×192
LCM(1800,1805) = 649800

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 1805

List of positive integer factors of 1805 that divides 1805 without a remainder.

1, 5, 19, 95, 361, 1805

Least Common Multiple of 1800 and 1805 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 1805, than apply into the LCM equation.

GCF(1800,1805) = 5
LCM(1800,1805) = ( 1800 × 1805) / 5
LCM(1800,1805) = 3249000 / 5
LCM(1800,1805) = 649800

Properties of LCM 1800 and 1805

(i) The LCM of 1805 and 1800 is associative

LCM of 1800 and 1805 = LCM of 1805 and 1800

Related Least Common Multiples of 1800

Related Least Common Multiples of 1805

Frequently Asked Questions on LCM of 1800 and 1805

1. What is the LCM of 1800 and 1805?

Answer: LCM of 1800 and 1805 is 649800.

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 1805?

Answer: Factors of 1805 are 1, 5, 19, 95, 361, 1805. There are 6 integers that are factors of 1805. The greatest factor of 1805 is 1805.

4. How to Find the LCM of 1800 and 1805?

Answer:

Least Common Multiple of 1800 and 1805 = 649800

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 1805

1805 = 5 x 19 x 19

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

LCM = 649800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 19 x 19

Step 4: Therefore, the least common multiple of 1800 and 1805 is 649800.