Least Common Multiple of 1800 and 1802

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 1802 the smallest integer that is 1621800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1800 and 1802 is 1621800.

LCM(1800,1802) = 1621800

LCM of 1800 and 1802

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

LCM of:
and

Least Common Multiple of 1800 and 1802

LCM of 1800 and 1802 is 1621800

Least common multiple can be found by multiplying the highest exponent prime factors of 1800 and 1802. First we will calculate the prime factors of 1800 and 1802.

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 1802


2 1802
17 901
53 53
1

Prime factors of 1802 are 2, 17,53. Prime factorization of 1802 in exponential form is:

1802 = 21×171×531

Now multiplying the highest exponent prime factors to calculate the LCM of 1800 and 1802.

LCM(1800,1802) = 23×32×52×171×531
LCM(1800,1802) = 1621800

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 1802

List of positive integer factors of 1802 that divides 1802 without a remainder.

1, 2, 17, 34, 53, 106, 901, 1802

Least Common Multiple of 1800 and 1802 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 1802, than apply into the LCM equation.

GCF(1800,1802) = 2
LCM(1800,1802) = ( 1800 × 1802) / 2
LCM(1800,1802) = 3243600 / 2
LCM(1800,1802) = 1621800

Properties of LCM 1800 and 1802

(i) The LCM of 1802 and 1800 is associative

LCM of 1800 and 1802 = LCM of 1802 and 1800

Related Least Common Multiples of 1800

Related Least Common Multiples of 1802

Frequently Asked Questions on LCM of 1800 and 1802

1. What is the LCM of 1800 and 1802?

Answer: LCM of 1800 and 1802 is 1621800.

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 1802?

Answer: Factors of 1802 are 1, 2, 17, 34, 53, 106, 901, 1802. There are 8 integers that are factors of 1802. The greatest factor of 1802 is 1802.

4. How to Find the LCM of 1800 and 1802?

Answer:

Least Common Multiple of 1800 and 1802 = 1621800

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 1802

1802 = 2 x 17 x 53

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

LCM = 1621800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 17 x 53

Step 4: Therefore, the least common multiple of 1800 and 1802 is 1621800.