Least Common Multiple of 1204 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 1204 and 1209 the smallest integer that is 1455636 that is divisible by both numbers.

Least Common Multiple (LCM) of 1204 and 1209 is 1455636.

LCM(1204,1209) = 1455636

LCM of 1204 and 1209

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

LCM of:
and

Least Common Multiple of 1204 and 1209

LCM of 1204 and 1209 is 1455636

Least common multiple can be found by multiplying the highest exponent prime factors of 1204 and 1209. First we will calculate the prime factors of 1204 and 1209.

Prime Factorization of 1204


2 1204
2 602
7 301
43 43
1

Prime factors of 1204 are 2, 7,43. Prime factorization of 1204 in exponential form is:

1204 = 22×71×431

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 1204 and 1209.

LCM(1204,1209) = 22×31×71×131×311×431
LCM(1204,1209) = 1455636

Factors of 1204

List of positive integer factors of 1204 that divides 1204 without a remainder.

1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602, 1204

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 1204 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 1204 and 1209, than apply into the LCM equation.

GCF(1204,1209) = 1
LCM(1204,1209) = ( 1204 × 1209) / 1
LCM(1204,1209) = 1455636 / 1
LCM(1204,1209) = 1455636

Properties of LCM 1204 and 1209

(i) The LCM of 1209 and 1204 is associative

LCM of 1204 and 1209 = LCM of 1209 and 1204

Related Least Common Multiples of 1204

Related Least Common Multiples of 1209

Frequently Asked Questions on LCM of 1204 and 1209

1. What is the LCM of 1204 and 1209?

Answer: LCM of 1204 and 1209 is 1455636.

2. What are the Factors of 1204?

Answer: Factors of 1204 are 1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602, 1204. There are 12 integers that are factors of 1204. The greatest factor of 1204 is 1204.

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 1204 and 1209?

Answer:

Least Common Multiple of 1204 and 1209 = 1455636

Step 1: Find the prime factorization of 1204

1204 = 2 x 2 x 7 x 43

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 = 1455636 = 2 x 2 x 3 x 7 x 13 x 31 x 43

Step 4: Therefore, the least common multiple of 1204 and 1209 is 1455636.