Least Common Multiple of 7224 and 7230

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7224 and 7230 the smallest integer that is 8704920 that is divisible by both numbers.

Least Common Multiple (LCM) of 7224 and 7230 is 8704920.

LCM(7224,7230) = 8704920

LCM of 7224 and 7230

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

LCM of:
and

Least Common Multiple of 7224 and 7230

LCM of 7224 and 7230 is 8704920

Least common multiple can be found by multiplying the highest exponent prime factors of 7224 and 7230. First we will calculate the prime factors of 7224 and 7230.

Prime Factorization of 7224


2 7224
2 3612
2 1806
3 903
7 301
43 43
1

Prime factors of 7224 are 2, 3, 7,43. Prime factorization of 7224 in exponential form is:

7224 = 23×31×71×431

Prime Factorization of 7230


2 7230
3 3615
5 1205
241 241
1

Prime factors of 7230 are 2, 3, 5,241. Prime factorization of 7230 in exponential form is:

7230 = 21×31×51×2411

Now multiplying the highest exponent prime factors to calculate the LCM of 7224 and 7230.

LCM(7224,7230) = 23×31×51×71×431×2411
LCM(7224,7230) = 8704920

Factors of 7224

List of positive integer factors of 7224 that divides 7224 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 43, 56, 84, 86, 129, 168, 172, 258, 301, 344, 516, 602, 903, 1032, 1204, 1806, 2408, 3612, 7224

Factors of 7230

List of positive integer factors of 7230 that divides 7230 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 241, 482, 723, 1205, 1446, 2410, 3615, 7230

Least Common Multiple of 7224 and 7230 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7224 and 7230, than apply into the LCM equation.

GCF(7224,7230) = 6
LCM(7224,7230) = ( 7224 × 7230) / 6
LCM(7224,7230) = 52229520 / 6
LCM(7224,7230) = 8704920

Properties of LCM 7224 and 7230

(i) The LCM of 7230 and 7224 is associative

LCM of 7224 and 7230 = LCM of 7230 and 7224

Related Least Common Multiples of 7224

Related Least Common Multiples of 7230

Frequently Asked Questions on LCM of 7224 and 7230

1. What is the LCM of 7224 and 7230?

Answer: LCM of 7224 and 7230 is 8704920.

2. What are the Factors of 7224?

Answer: Factors of 7224 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 43, 56, 84, 86, 129, 168, 172, 258, 301, 344, 516, 602, 903, 1032, 1204, 1806, 2408, 3612, 7224. There are 32 integers that are factors of 7224. The greatest factor of 7224 is 7224.

3. What are the Factors of 7230?

Answer: Factors of 7230 are 1, 2, 3, 5, 6, 10, 15, 30, 241, 482, 723, 1205, 1446, 2410, 3615, 7230. There are 16 integers that are factors of 7230. The greatest factor of 7230 is 7230.

4. How to Find the LCM of 7224 and 7230?

Answer:

Least Common Multiple of 7224 and 7230 = 8704920

Step 1: Find the prime factorization of 7224

7224 = 2 x 2 x 2 x 3 x 7 x 43

Step 2: Find the prime factorization of 7230

7230 = 2 x 3 x 5 x 241

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

LCM = 8704920 = 2 x 2 x 2 x 3 x 5 x 7 x 43 x 241

Step 4: Therefore, the least common multiple of 7224 and 7230 is 8704920.