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 565 the smallest integer that is 318660 that is divisible by both numbers.
Least Common Multiple (LCM) of 564 and 565 is 318660.
LCM(564,565) = 318660
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 565. First we will calculate the prime factors of 564 and 565.
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 565
5 | 565 |
113 | 113 |
1 |
Prime factors of 565 are 5,113. Prime factorization of 565 in exponential form is:
565 = 51×1131
Now multiplying the highest exponent prime factors to calculate the LCM of 564 and 565.
LCM(564,565) = 22×31×51×471×1131
LCM(564,565) = 318660
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 565
List of positive integer factors of 565 that divides 565 without a remainder.
1, 5, 113, 565
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 564 and 565, than apply into the LCM equation.
GCF(564,565) = 1
LCM(564,565) = ( 564 × 565) / 1
LCM(564,565) = 318660 / 1
LCM(564,565) = 318660
(i) The LCM of 565 and 564 is associative
LCM of 564 and 565 = LCM of 565 and 564
1. What is the LCM of 564 and 565?
Answer: LCM of 564 and 565 is 318660.
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 565?
Answer: Factors of 565 are 1, 5, 113, 565. There are 4 integers that are factors of 565. The greatest factor of 565 is 565.
4. How to Find the LCM of 564 and 565?
Answer:
Least Common Multiple of 564 and 565 = 318660
Step 1: Find the prime factorization of 564
564 = 2 x 2 x 3 x 47
Step 2: Find the prime factorization of 565
565 = 5 x 113
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 318660 = 2 x 2 x 3 x 5 x 47 x 113
Step 4: Therefore, the least common multiple of 564 and 565 is 318660.