Least Common Multiple of 560 and 567

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 567 the smallest integer that is 45360 that is divisible by both numbers.

Least Common Multiple (LCM) of 560 and 567 is 45360.

LCM(560,567) = 45360

LCM of 560 and 567

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

LCM of:
and

Least Common Multiple of 560 and 567

LCM of 560 and 567 is 45360

Least common multiple can be found by multiplying the highest exponent prime factors of 560 and 567. First we will calculate the prime factors of 560 and 567.

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 567


3 567
3 189
3 63
3 21
7 7
1

Prime factors of 567 are 3,7. Prime factorization of 567 in exponential form is:

567 = 34×71

Now multiplying the highest exponent prime factors to calculate the LCM of 560 and 567.

LCM(560,567) = 24×34×51×71
LCM(560,567) = 45360

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 567

List of positive integer factors of 567 that divides 567 without a remainder.

1, 3, 7, 9, 21, 27, 63, 81, 189, 567

Least Common Multiple of 560 and 567 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 567, than apply into the LCM equation.

GCF(560,567) = 7
LCM(560,567) = ( 560 × 567) / 7
LCM(560,567) = 317520 / 7
LCM(560,567) = 45360

Properties of LCM 560 and 567

(i) The LCM of 567 and 560 is associative

LCM of 560 and 567 = LCM of 567 and 560

Related Least Common Multiples of 560

Related Least Common Multiples of 567

Frequently Asked Questions on LCM of 560 and 567

1. What is the LCM of 560 and 567?

Answer: LCM of 560 and 567 is 45360.

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 567?

Answer: Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567. There are 10 integers that are factors of 567. The greatest factor of 567 is 567.

4. How to Find the LCM of 560 and 567?

Answer:

Least Common Multiple of 560 and 567 = 45360

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 567

567 = 3 x 3 x 3 x 3 x 7

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

LCM = 45360 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 560 and 567 is 45360.