Least Common Multiple of 7200 and 7204

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7200 and 7204 the smallest integer that is 12967200 that is divisible by both numbers.

Least Common Multiple (LCM) of 7200 and 7204 is 12967200.

LCM(7200,7204) = 12967200

LCM of 7200 and 7204

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

LCM of:
and

Least Common Multiple of 7200 and 7204

LCM of 7200 and 7204 is 12967200

Least common multiple can be found by multiplying the highest exponent prime factors of 7200 and 7204. First we will calculate the prime factors of 7200 and 7204.

Prime Factorization of 7200


2 7200
2 3600
2 1800
2 900
2 450
3 225
3 75
5 25
5 5
1

Prime factors of 7200 are 2, 3,5. Prime factorization of 7200 in exponential form is:

7200 = 25×32×52

Prime Factorization of 7204


2 7204
2 3602
1801 1801
1

Prime factors of 7204 are 2,1801. Prime factorization of 7204 in exponential form is:

7204 = 22×18011

Now multiplying the highest exponent prime factors to calculate the LCM of 7200 and 7204.

LCM(7200,7204) = 25×32×52×18011
LCM(7200,7204) = 12967200

Factors of 7200

List of positive integer factors of 7200 that divides 7200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 800, 900, 1200, 1440, 1800, 2400, 3600, 7200

Factors of 7204

List of positive integer factors of 7204 that divides 7204 without a remainder.

1, 2, 4, 1801, 3602, 7204

Least Common Multiple of 7200 and 7204 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7200 and 7204, than apply into the LCM equation.

GCF(7200,7204) = 4
LCM(7200,7204) = ( 7200 × 7204) / 4
LCM(7200,7204) = 51868800 / 4
LCM(7200,7204) = 12967200

Properties of LCM 7200 and 7204

(i) The LCM of 7204 and 7200 is associative

LCM of 7200 and 7204 = LCM of 7204 and 7200

Related Least Common Multiples of 7200

Related Least Common Multiples of 7204

Frequently Asked Questions on LCM of 7200 and 7204

1. What is the LCM of 7200 and 7204?

Answer: LCM of 7200 and 7204 is 12967200.

2. What are the Factors of 7200?

Answer: Factors of 7200 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 800, 900, 1200, 1440, 1800, 2400, 3600, 7200. There are 54 integers that are factors of 7200. The greatest factor of 7200 is 7200.

3. What are the Factors of 7204?

Answer: Factors of 7204 are 1, 2, 4, 1801, 3602, 7204. There are 6 integers that are factors of 7204. The greatest factor of 7204 is 7204.

4. How to Find the LCM of 7200 and 7204?

Answer:

Least Common Multiple of 7200 and 7204 = 12967200

Step 1: Find the prime factorization of 7200

7200 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 7204

7204 = 2 x 2 x 1801

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

LCM = 12967200 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 1801

Step 4: Therefore, the least common multiple of 7200 and 7204 is 12967200.