Least Common Multiple of 7224 and 7232

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 7232 the smallest integer that is 6530496 that is divisible by both numbers.

Least Common Multiple (LCM) of 7224 and 7232 is 6530496.

LCM(7224,7232) = 6530496

LCM of 7224 and 7232

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

LCM of:
and

Least Common Multiple of 7224 and 7232

LCM of 7224 and 7232 is 6530496

Least common multiple can be found by multiplying the highest exponent prime factors of 7224 and 7232. First we will calculate the prime factors of 7224 and 7232.

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 7232


2 7232
2 3616
2 1808
2 904
2 452
2 226
113 113
1

Prime factors of 7232 are 2,113. Prime factorization of 7232 in exponential form is:

7232 = 26×1131

Now multiplying the highest exponent prime factors to calculate the LCM of 7224 and 7232.

LCM(7224,7232) = 26×31×71×431×1131
LCM(7224,7232) = 6530496

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 7232

List of positive integer factors of 7232 that divides 7232 without a remainder.

1, 2, 4, 8, 16, 32, 64, 113, 226, 452, 904, 1808, 3616, 7232

Least Common Multiple of 7224 and 7232 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 7232, than apply into the LCM equation.

GCF(7224,7232) = 8
LCM(7224,7232) = ( 7224 × 7232) / 8
LCM(7224,7232) = 52243968 / 8
LCM(7224,7232) = 6530496

Properties of LCM 7224 and 7232

(i) The LCM of 7232 and 7224 is associative

LCM of 7224 and 7232 = LCM of 7232 and 7224

Related Least Common Multiples of 7224

Related Least Common Multiples of 7232

Frequently Asked Questions on LCM of 7224 and 7232

1. What is the LCM of 7224 and 7232?

Answer: LCM of 7224 and 7232 is 6530496.

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 7232?

Answer: Factors of 7232 are 1, 2, 4, 8, 16, 32, 64, 113, 226, 452, 904, 1808, 3616, 7232. There are 14 integers that are factors of 7232. The greatest factor of 7232 is 7232.

4. How to Find the LCM of 7224 and 7232?

Answer:

Least Common Multiple of 7224 and 7232 = 6530496

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 7232

7232 = 2 x 2 x 2 x 2 x 2 x 2 x 113

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

LCM = 6530496 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 43 x 113

Step 4: Therefore, the least common multiple of 7224 and 7232 is 6530496.