Least Common Multiple of 560 and 564

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 560 and 564 the smallest integer that is 78960 that is divisible by both numbers.

Least Common Multiple (LCM) of 560 and 564 is 78960.

LCM(560,564) = 78960

LCM of 560 and 564

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

LCM of:
and

Least Common Multiple of 560 and 564

LCM of 560 and 564 is 78960

Least common multiple can be found by multiplying the highest exponent prime factors of 560 and 564. First we will calculate the prime factors of 560 and 564.

Prime Factorization of 560


2 560
2 280
2 140
2 70
5 35
7 7
1

Prime factors of 560 are 2, 5,7. Prime factorization of 560 in exponential form is:

560 = 24×51×71

Prime Factorization of 564


2 564
2 282
3 141
47 47
1

Prime factors of 564 are 2, 3,47. Prime factorization of 564 in exponential form is:

564 = 22×31×471

Now multiplying the highest exponent prime factors to calculate the LCM of 560 and 564.

LCM(560,564) = 24×31×51×71×471
LCM(560,564) = 78960

Factors of 560

List of positive integer factors of 560 that divides 560 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560

Factors of 564

List of positive integer factors of 564 that divides 564 without a remainder.

1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564

Least Common Multiple of 560 and 564 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 560 and 564, than apply into the LCM equation.

GCF(560,564) = 4
LCM(560,564) = ( 560 × 564) / 4
LCM(560,564) = 315840 / 4
LCM(560,564) = 78960

Properties of LCM 560 and 564

(i) The LCM of 564 and 560 is associative

LCM of 560 and 564 = LCM of 564 and 560

Related Least Common Multiples of 560

Related Least Common Multiples of 564

Frequently Asked Questions on LCM of 560 and 564

1. What is the LCM of 560 and 564?

Answer: LCM of 560 and 564 is 78960.

2. What are the Factors of 560?

Answer: Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560. There are 20 integers that are factors of 560. The greatest factor of 560 is 560.

3. What are the Factors of 564?

Answer: Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564. There are 12 integers that are factors of 564. The greatest factor of 564 is 564.

4. How to Find the LCM of 560 and 564?

Answer:

Least Common Multiple of 560 and 564 = 78960

Step 1: Find the prime factorization of 560

560 = 2 x 2 x 2 x 2 x 5 x 7

Step 2: Find the prime factorization of 564

564 = 2 x 2 x 3 x 47

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

LCM = 78960 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 47

Step 4: Therefore, the least common multiple of 560 and 564 is 78960.