Least Common Multiple of 7200 and 7208

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 7208 the smallest integer that is 6487200 that is divisible by both numbers.

Least Common Multiple (LCM) of 7200 and 7208 is 6487200.

LCM(7200,7208) = 6487200

LCM of 7200 and 7208

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

LCM of:
and

Least Common Multiple of 7200 and 7208

LCM of 7200 and 7208 is 6487200

Least common multiple can be found by multiplying the highest exponent prime factors of 7200 and 7208. First we will calculate the prime factors of 7200 and 7208.

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 7208


2 7208
2 3604
2 1802
17 901
53 53
1

Prime factors of 7208 are 2, 17,53. Prime factorization of 7208 in exponential form is:

7208 = 23×171×531

Now multiplying the highest exponent prime factors to calculate the LCM of 7200 and 7208.

LCM(7200,7208) = 25×32×52×171×531
LCM(7200,7208) = 6487200

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 7208

List of positive integer factors of 7208 that divides 7208 without a remainder.

1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208

Least Common Multiple of 7200 and 7208 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 7208, than apply into the LCM equation.

GCF(7200,7208) = 8
LCM(7200,7208) = ( 7200 × 7208) / 8
LCM(7200,7208) = 51897600 / 8
LCM(7200,7208) = 6487200

Properties of LCM 7200 and 7208

(i) The LCM of 7208 and 7200 is associative

LCM of 7200 and 7208 = LCM of 7208 and 7200

Related Least Common Multiples of 7200

Related Least Common Multiples of 7208

Frequently Asked Questions on LCM of 7200 and 7208

1. What is the LCM of 7200 and 7208?

Answer: LCM of 7200 and 7208 is 6487200.

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 7208?

Answer: Factors of 7208 are 1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208. There are 16 integers that are factors of 7208. The greatest factor of 7208 is 7208.

4. How to Find the LCM of 7200 and 7208?

Answer:

Least Common Multiple of 7200 and 7208 = 6487200

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 7208

7208 = 2 x 2 x 2 x 17 x 53

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

LCM = 6487200 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 17 x 53

Step 4: Therefore, the least common multiple of 7200 and 7208 is 6487200.