Least Common Multiple of 576 and 584

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 576 and 584 the smallest integer that is 42048 that is divisible by both numbers.

Least Common Multiple (LCM) of 576 and 584 is 42048.

LCM(576,584) = 42048

LCM of 576 and 584

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

LCM of:
and

Least Common Multiple of 576 and 584

LCM of 576 and 584 is 42048

Least common multiple can be found by multiplying the highest exponent prime factors of 576 and 584. First we will calculate the prime factors of 576 and 584.

Prime Factorization of 576


2 576
2 288
2 144
2 72
2 36
2 18
3 9
3 3
1

Prime factors of 576 are 2,3. Prime factorization of 576 in exponential form is:

576 = 26×32

Prime Factorization of 584


2 584
2 292
2 146
73 73
1

Prime factors of 584 are 2,73. Prime factorization of 584 in exponential form is:

584 = 23×731

Now multiplying the highest exponent prime factors to calculate the LCM of 576 and 584.

LCM(576,584) = 26×32×731
LCM(576,584) = 42048

Factors of 576

List of positive integer factors of 576 that divides 576 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576

Factors of 584

List of positive integer factors of 584 that divides 584 without a remainder.

1, 2, 4, 8, 73, 146, 292, 584

Least Common Multiple of 576 and 584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 576 and 584, than apply into the LCM equation.

GCF(576,584) = 8
LCM(576,584) = ( 576 × 584) / 8
LCM(576,584) = 336384 / 8
LCM(576,584) = 42048

Properties of LCM 576 and 584

(i) The LCM of 584 and 576 is associative

LCM of 576 and 584 = LCM of 584 and 576

Related Least Common Multiples of 576

Related Least Common Multiples of 584

Frequently Asked Questions on LCM of 576 and 584

1. What is the LCM of 576 and 584?

Answer: LCM of 576 and 584 is 42048.

2. What are the Factors of 576?

Answer: Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576. There are 21 integers that are factors of 576. The greatest factor of 576 is 576.

3. What are the Factors of 584?

Answer: Factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584. There are 8 integers that are factors of 584. The greatest factor of 584 is 584.

4. How to Find the LCM of 576 and 584?

Answer:

Least Common Multiple of 576 and 584 = 42048

Step 1: Find the prime factorization of 576

576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 584

584 = 2 x 2 x 2 x 73

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

LCM = 42048 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 73

Step 4: Therefore, the least common multiple of 576 and 584 is 42048.