Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 564 and 566 the smallest integer that is 159612 that is divisible by both numbers.
Least Common Multiple (LCM) of 564 and 566 is 159612.
LCM(564,566) = 159612
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 564 and 566. First we will calculate the prime factors of 564 and 566.
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
Prime Factorization of 566
2 | 566 |
283 | 283 |
1 |
Prime factors of 566 are 2,283. Prime factorization of 566 in exponential form is:
566 = 21×2831
Now multiplying the highest exponent prime factors to calculate the LCM of 564 and 566.
LCM(564,566) = 22×31×471×2831
LCM(564,566) = 159612
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
Factors of 566
List of positive integer factors of 566 that divides 566 without a remainder.
1, 2, 283, 566
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 564 and 566, than apply into the LCM equation.
GCF(564,566) = 2
LCM(564,566) = ( 564 × 566) / 2
LCM(564,566) = 319224 / 2
LCM(564,566) = 159612
(i) The LCM of 566 and 564 is associative
LCM of 564 and 566 = LCM of 566 and 564
1. What is the LCM of 564 and 566?
Answer: LCM of 564 and 566 is 159612.
2. 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.
3. What are the Factors of 566?
Answer: Factors of 566 are 1, 2, 283, 566. There are 4 integers that are factors of 566. The greatest factor of 566 is 566.
4. How to Find the LCM of 564 and 566?
Answer:
Least Common Multiple of 564 and 566 = 159612
Step 1: Find the prime factorization of 564
564 = 2 x 2 x 3 x 47
Step 2: Find the prime factorization of 566
566 = 2 x 283
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 159612 = 2 x 2 x 3 x 47 x 283
Step 4: Therefore, the least common multiple of 564 and 566 is 159612.