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 567 the smallest integer that is 106596 that is divisible by both numbers.
Least Common Multiple (LCM) of 564 and 567 is 106596.
LCM(564,567) = 106596
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 567. First we will calculate the prime factors of 564 and 567.
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 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 564 and 567.
LCM(564,567) = 22×34×71×471
LCM(564,567) = 106596
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 567
List of positive integer factors of 567 that divides 567 without a remainder.
1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 564 and 567, than apply into the LCM equation.
GCF(564,567) = 3
LCM(564,567) = ( 564 × 567) / 3
LCM(564,567) = 319788 / 3
LCM(564,567) = 106596
(i) The LCM of 567 and 564 is associative
LCM of 564 and 567 = LCM of 567 and 564
1. What is the LCM of 564 and 567?
Answer: LCM of 564 and 567 is 106596.
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 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 564 and 567?
Answer:
Least Common Multiple of 564 and 567 = 106596
Step 1: Find the prime factorization of 564
564 = 2 x 2 x 3 x 47
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 = 106596 = 2 x 2 x 3 x 3 x 3 x 3 x 7 x 47
Step 4: Therefore, the least common multiple of 564 and 567 is 106596.