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 565 the smallest integer that is 316965 that is divisible by both numbers.
Least Common Multiple (LCM) of 561 and 565 is 316965.
LCM(561,565) = 316965
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 561 and 565. First we will calculate the prime factors of 561 and 565.
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 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 561 and 565.
LCM(561,565) = 31×51×111×171×1131
LCM(561,565) = 316965
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 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 561 and 565, than apply into the LCM equation.
GCF(561,565) = 1
LCM(561,565) = ( 561 × 565) / 1
LCM(561,565) = 316965 / 1
LCM(561,565) = 316965
(i) The LCM of 565 and 561 is associative
LCM of 561 and 565 = LCM of 565 and 561
1. What is the LCM of 561 and 565?
Answer: LCM of 561 and 565 is 316965.
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 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 561 and 565?
Answer:
Least Common Multiple of 561 and 565 = 316965
Step 1: Find the prime factorization of 561
561 = 3 x 11 x 17
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 = 316965 = 3 x 5 x 11 x 17 x 113
Step 4: Therefore, the least common multiple of 561 and 565 is 316965.