Least Common Multiple of 561 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 561 and 564 the smallest integer that is 105468 that is divisible by both numbers.

Least Common Multiple (LCM) of 561 and 564 is 105468.

LCM(561,564) = 105468

LCM of 561 and 564

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

LCM of:
and

Least Common Multiple of 561 and 564

LCM of 561 and 564 is 105468

Least common multiple can be found by multiplying the highest exponent prime factors of 561 and 564. First we will calculate the prime factors of 561 and 564.

Prime Factorization of 561


3 561
11 187
17 17
1

Prime factors of 561 are 3, 11,17. Prime factorization of 561 in exponential form is:

561 = 31×111×171

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 561 and 564.

LCM(561,564) = 22×31×111×171×471
LCM(561,564) = 105468

Factors of 561

List of positive integer factors of 561 that divides 561 without a remainder.

1, 3, 11, 17, 33, 51, 187, 561

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 561 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 561 and 564, than apply into the LCM equation.

GCF(561,564) = 3
LCM(561,564) = ( 561 × 564) / 3
LCM(561,564) = 316404 / 3
LCM(561,564) = 105468

Properties of LCM 561 and 564

(i) The LCM of 564 and 561 is associative

LCM of 561 and 564 = LCM of 564 and 561

Related Least Common Multiples of 561

Related Least Common Multiples of 564

Frequently Asked Questions on LCM of 561 and 564

1. What is the LCM of 561 and 564?

Answer: LCM of 561 and 564 is 105468.

2. What are the Factors of 561?

Answer: Factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561. There are 8 integers that are factors of 561. The greatest factor of 561 is 561.

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 561 and 564?

Answer:

Least Common Multiple of 561 and 564 = 105468

Step 1: Find the prime factorization of 561

561 = 3 x 11 x 17

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 = 105468 = 2 x 2 x 3 x 11 x 17 x 47

Step 4: Therefore, the least common multiple of 561 and 564 is 105468.