Least Common Multiple of 1205 and 1209

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1205 and 1209 the smallest integer that is 1456845 that is divisible by both numbers.

Least Common Multiple (LCM) of 1205 and 1209 is 1456845.

LCM(1205,1209) = 1456845

LCM of 1205 and 1209

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

LCM of:
and

Least Common Multiple of 1205 and 1209

LCM of 1205 and 1209 is 1456845

Least common multiple can be found by multiplying the highest exponent prime factors of 1205 and 1209. First we will calculate the prime factors of 1205 and 1209.

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

Prime Factorization of 1209


3 1209
13 403
31 31
1

Prime factors of 1209 are 3, 13,31. Prime factorization of 1209 in exponential form is:

1209 = 31×131×311

Now multiplying the highest exponent prime factors to calculate the LCM of 1205 and 1209.

LCM(1205,1209) = 31×51×131×311×2411
LCM(1205,1209) = 1456845

Factors of 1205

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

1, 5, 241, 1205

Factors of 1209

List of positive integer factors of 1209 that divides 1209 without a remainder.

1, 3, 13, 31, 39, 93, 403, 1209

Least Common Multiple of 1205 and 1209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1205 and 1209, than apply into the LCM equation.

GCF(1205,1209) = 1
LCM(1205,1209) = ( 1205 × 1209) / 1
LCM(1205,1209) = 1456845 / 1
LCM(1205,1209) = 1456845

Properties of LCM 1205 and 1209

(i) The LCM of 1209 and 1205 is associative

LCM of 1205 and 1209 = LCM of 1209 and 1205

Related Least Common Multiples of 1205

Related Least Common Multiples of 1209

Frequently Asked Questions on LCM of 1205 and 1209

1. What is the LCM of 1205 and 1209?

Answer: LCM of 1205 and 1209 is 1456845.

2. 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.

3. What are the Factors of 1209?

Answer: Factors of 1209 are 1, 3, 13, 31, 39, 93, 403, 1209. There are 8 integers that are factors of 1209. The greatest factor of 1209 is 1209.

4. How to Find the LCM of 1205 and 1209?

Answer:

Least Common Multiple of 1205 and 1209 = 1456845

Step 1: Find the prime factorization of 1205

1205 = 5 x 241

Step 2: Find the prime factorization of 1209

1209 = 3 x 13 x 31

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

LCM = 1456845 = 3 x 5 x 13 x 31 x 241

Step 4: Therefore, the least common multiple of 1205 and 1209 is 1456845.