Least Common Multiple of 7584 and 7588

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7584 and 7588 the smallest integer that is 14386848 that is divisible by both numbers.

Least Common Multiple (LCM) of 7584 and 7588 is 14386848.

LCM(7584,7588) = 14386848

LCM of 7584 and 7588

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

LCM of:
and

Least Common Multiple of 7584 and 7588

LCM of 7584 and 7588 is 14386848

Least common multiple can be found by multiplying the highest exponent prime factors of 7584 and 7588. First we will calculate the prime factors of 7584 and 7588.

Prime Factorization of 7584


2 7584
2 3792
2 1896
2 948
2 474
3 237
79 79
1

Prime factors of 7584 are 2, 3,79. Prime factorization of 7584 in exponential form is:

7584 = 25×31×791

Prime Factorization of 7588


2 7588
2 3794
7 1897
271 271
1

Prime factors of 7588 are 2, 7,271. Prime factorization of 7588 in exponential form is:

7588 = 22×71×2711

Now multiplying the highest exponent prime factors to calculate the LCM of 7584 and 7588.

LCM(7584,7588) = 25×31×71×791×2711
LCM(7584,7588) = 14386848

Factors of 7584

List of positive integer factors of 7584 that divides 7584 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 79, 96, 158, 237, 316, 474, 632, 948, 1264, 1896, 2528, 3792, 7584

Factors of 7588

List of positive integer factors of 7588 that divides 7588 without a remainder.

1, 2, 4, 7, 14, 28, 271, 542, 1084, 1897, 3794, 7588

Least Common Multiple of 7584 and 7588 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7584 and 7588, than apply into the LCM equation.

GCF(7584,7588) = 4
LCM(7584,7588) = ( 7584 × 7588) / 4
LCM(7584,7588) = 57547392 / 4
LCM(7584,7588) = 14386848

Properties of LCM 7584 and 7588

(i) The LCM of 7588 and 7584 is associative

LCM of 7584 and 7588 = LCM of 7588 and 7584

Related Least Common Multiples of 7584

Related Least Common Multiples of 7588

Frequently Asked Questions on LCM of 7584 and 7588

1. What is the LCM of 7584 and 7588?

Answer: LCM of 7584 and 7588 is 14386848.

2. What are the Factors of 7584?

Answer: Factors of 7584 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 79, 96, 158, 237, 316, 474, 632, 948, 1264, 1896, 2528, 3792, 7584. There are 24 integers that are factors of 7584. The greatest factor of 7584 is 7584.

3. What are the Factors of 7588?

Answer: Factors of 7588 are 1, 2, 4, 7, 14, 28, 271, 542, 1084, 1897, 3794, 7588. There are 12 integers that are factors of 7588. The greatest factor of 7588 is 7588.

4. How to Find the LCM of 7584 and 7588?

Answer:

Least Common Multiple of 7584 and 7588 = 14386848

Step 1: Find the prime factorization of 7584

7584 = 2 x 2 x 2 x 2 x 2 x 3 x 79

Step 2: Find the prime factorization of 7588

7588 = 2 x 2 x 7 x 271

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

LCM = 14386848 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 79 x 271

Step 4: Therefore, the least common multiple of 7584 and 7588 is 14386848.