Least Common Multiple of 1800 and 1808

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 1808 the smallest integer that is 406800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1800 and 1808 is 406800.

LCM(1800,1808) = 406800

LCM of 1800 and 1808

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

LCM of:
and

Least Common Multiple of 1800 and 1808

LCM of 1800 and 1808 is 406800

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1808. First we will calculate the prime factors of 1800 and 1808.

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 1808


2 1808
2 904
2 452
2 226
113 113
1

Prime factors of 1808 are 2,113. Prime factorization of 1808 in exponential form is:

1808 = 24×1131

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1808.

LCM(1800,1808) = 24×32×52×1131
LCM(1800,1808) = 406800

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 1808

List of positive integer factors of 1808 that divides 1808 without a remainder.

1, 2, 4, 8, 16, 113, 226, 452, 904, 1808

Least Common Multiple of 1800 and 1808 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 1808, than apply into the LCM equation.

GCF(1800,1808) = 8
LCM(1800,1808) = ( 1800 × 1808) / 8
LCM(1800,1808) = 3254400 / 8
LCM(1800,1808) = 406800

Properties of LCM 1800 and 1808

(i) The LCM of 1808 and 1800 is associative

LCM of 1800 and 1808 = LCM of 1808 and 1800

Related Least Common Multiples of 1800

Related Least Common Multiples of 1808

Frequently Asked Questions on LCM of 1800 and 1808

1. What is the LCM of 1800 and 1808?

Answer: LCM of 1800 and 1808 is 406800.

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 1808?

Answer: Factors of 1808 are 1, 2, 4, 8, 16, 113, 226, 452, 904, 1808. There are 10 integers that are factors of 1808. The greatest factor of 1808 is 1808.

4. How to Find the LCM of 1800 and 1808?

Answer:

Least Common Multiple of 1800 and 1808 = 406800

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 1808

1808 = 2 x 2 x 2 x 2 x 113

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

LCM = 406800 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 113

Step 4: Therefore, the least common multiple of 1800 and 1808 is 406800.