Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 554 and 561 the smallest integer that is 310794 that is divisible by both numbers.
Least Common Multiple (LCM) of 554 and 561 is 310794.
LCM(554,561) = 310794
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 554 and 561. First we will calculate the prime factors of 554 and 561.
Prime Factorization of 554
2 | 554 |
277 | 277 |
1 |
Prime factors of 554 are 2,277. Prime factorization of 554 in exponential form is:
554 = 21×2771
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
Now multiplying the highest exponent prime factors to calculate the LCM of 554 and 561.
LCM(554,561) = 21×31×111×171×2771
LCM(554,561) = 310794
Factors of 554
List of positive integer factors of 554 that divides 554 without a remainder.
1, 2, 277, 554
Factors of 561
List of positive integer factors of 561 that divides 561 without a remainder.
1, 3, 11, 17, 33, 51, 187, 561
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 554 and 561, than apply into the LCM equation.
GCF(554,561) = 1
LCM(554,561) = ( 554 × 561) / 1
LCM(554,561) = 310794 / 1
LCM(554,561) = 310794
(i) The LCM of 561 and 554 is associative
LCM of 554 and 561 = LCM of 561 and 554
1. What is the LCM of 554 and 561?
Answer: LCM of 554 and 561 is 310794.
2. What are the Factors of 554?
Answer: Factors of 554 are 1, 2, 277, 554. There are 4 integers that are factors of 554. The greatest factor of 554 is 554.
3. 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.
4. How to Find the LCM of 554 and 561?
Answer:
Least Common Multiple of 554 and 561 = 310794
Step 1: Find the prime factorization of 554
554 = 2 x 277
Step 2: Find the prime factorization of 561
561 = 3 x 11 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 310794 = 2 x 3 x 11 x 17 x 277
Step 4: Therefore, the least common multiple of 554 and 561 is 310794.