Least Common Multiple of 576 and 578

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 578 the smallest integer that is 166464 that is divisible by both numbers.

Least Common Multiple (LCM) of 576 and 578 is 166464.

LCM(576,578) = 166464

LCM of 576 and 578

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

LCM of:
and

Least Common Multiple of 576 and 578

LCM of 576 and 578 is 166464

Least common multiple can be found by multiplying the highest exponent prime factors of 576 and 578. First we will calculate the prime factors of 576 and 578.

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 578


2 578
17 289
17 17
1

Prime factors of 578 are 2,17. Prime factorization of 578 in exponential form is:

578 = 21×172

Now multiplying the highest exponent prime factors to calculate the LCM of 576 and 578.

LCM(576,578) = 26×32×172
LCM(576,578) = 166464

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 578

List of positive integer factors of 578 that divides 578 without a remainder.

1, 2, 17, 34, 289, 578

Least Common Multiple of 576 and 578 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 578, than apply into the LCM equation.

GCF(576,578) = 2
LCM(576,578) = ( 576 × 578) / 2
LCM(576,578) = 332928 / 2
LCM(576,578) = 166464

Properties of LCM 576 and 578

(i) The LCM of 578 and 576 is associative

LCM of 576 and 578 = LCM of 578 and 576

Related Least Common Multiples of 576

Related Least Common Multiples of 578

Frequently Asked Questions on LCM of 576 and 578

1. What is the LCM of 576 and 578?

Answer: LCM of 576 and 578 is 166464.

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 578?

Answer: Factors of 578 are 1, 2, 17, 34, 289, 578. There are 6 integers that are factors of 578. The greatest factor of 578 is 578.

4. How to Find the LCM of 576 and 578?

Answer:

Least Common Multiple of 576 and 578 = 166464

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 578

578 = 2 x 17 x 17

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

LCM = 166464 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 17 x 17

Step 4: Therefore, the least common multiple of 576 and 578 is 166464.