Least Common Multiple of 1200 and 1204

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 1204 the smallest integer that is 361200 that is divisible by both numbers.

Least Common Multiple (LCM) of 1200 and 1204 is 361200.

LCM(1200,1204) = 361200

LCM of 1200 and 1204

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

LCM of:
and

Least Common Multiple of 1200 and 1204

LCM of 1200 and 1204 is 361200

Least common multiple can be found by multiplying the highest exponent prime factors of 1200 and 1204. First we will calculate the prime factors of 1200 and 1204.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 1200 and 1204.

LCM(1200,1204) = 24×31×52×71×431
LCM(1200,1204) = 361200

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 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

Least Common Multiple of 1200 and 1204 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 1204, than apply into the LCM equation.

GCF(1200,1204) = 4
LCM(1200,1204) = ( 1200 × 1204) / 4
LCM(1200,1204) = 1444800 / 4
LCM(1200,1204) = 361200

Properties of LCM 1200 and 1204

(i) The LCM of 1204 and 1200 is associative

LCM of 1200 and 1204 = LCM of 1204 and 1200

Related Least Common Multiples of 1200

Related Least Common Multiples of 1204

Frequently Asked Questions on LCM of 1200 and 1204

1. What is the LCM of 1200 and 1204?

Answer: LCM of 1200 and 1204 is 361200.

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 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.

4. How to Find the LCM of 1200 and 1204?

Answer:

Least Common Multiple of 1200 and 1204 = 361200

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 1204

1204 = 2 x 2 x 7 x 43

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

LCM = 361200 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 43

Step 4: Therefore, the least common multiple of 1200 and 1204 is 361200.