Least Common Multiple of 1200 and 1205

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1200 and 1205 the smallest integer that is 289200 that is divisible by both numbers.

Least Common Multiple (LCM) of 1200 and 1205 is 289200.

LCM(1200,1205) = 289200

LCM of 1200 and 1205

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

LCM of:
and

Least Common Multiple of 1200 and 1205

LCM of 1200 and 1205 is 289200

Least common multiple can be found by multiplying the highest exponent prime factors of 1200 and 1205. First we will calculate the prime factors of 1200 and 1205.

Prime Factorization of 1200


2 1200
2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 1200 are 2, 3,5. Prime factorization of 1200 in exponential form is:

1200 = 24×31×52

Prime Factorization of 1205


5 1205
241 241
1

Prime factors of 1205 are 5,241. Prime factorization of 1205 in exponential form is:

1205 = 51×2411

Now multiplying the highest exponent prime factors to calculate the LCM of 1200 and 1205.

LCM(1200,1205) = 24×31×52×2411
LCM(1200,1205) = 289200

Factors of 1200

List of positive integer factors of 1200 that divides 1200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

Factors of 1205

List of positive integer factors of 1205 that divides 1205 without a remainder.

1, 5, 241, 1205

Least Common Multiple of 1200 and 1205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1200 and 1205, than apply into the LCM equation.

GCF(1200,1205) = 5
LCM(1200,1205) = ( 1200 × 1205) / 5
LCM(1200,1205) = 1446000 / 5
LCM(1200,1205) = 289200

Properties of LCM 1200 and 1205

(i) The LCM of 1205 and 1200 is associative

LCM of 1200 and 1205 = LCM of 1205 and 1200

Related Least Common Multiples of 1200

Related Least Common Multiples of 1205

Frequently Asked Questions on LCM of 1200 and 1205

1. What is the LCM of 1200 and 1205?

Answer: LCM of 1200 and 1205 is 289200.

2. What are the Factors of 1200?

Answer: Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200. There are 30 integers that are factors of 1200. The greatest factor of 1200 is 1200.

3. What are the Factors of 1205?

Answer: Factors of 1205 are 1, 5, 241, 1205. There are 4 integers that are factors of 1205. The greatest factor of 1205 is 1205.

4. How to Find the LCM of 1200 and 1205?

Answer:

Least Common Multiple of 1200 and 1205 = 289200

Step 1: Find the prime factorization of 1200

1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 1205

1205 = 5 x 241

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

LCM = 289200 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 241

Step 4: Therefore, the least common multiple of 1200 and 1205 is 289200.