Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 255 and 259 the smallest integer that is 66045 that is divisible by both numbers.
Least Common Multiple (LCM) of 255 and 259 is 66045.
LCM(255,259) = 66045
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 255 and 259. First we will calculate the prime factors of 255 and 259.
Prime Factorization of 255
3 | 255 |
5 | 85 |
17 | 17 |
1 |
Prime factors of 255 are 3, 5,17. Prime factorization of 255 in exponential form is:
255 = 31×51×171
Prime Factorization of 259
7 | 259 |
37 | 37 |
1 |
Prime factors of 259 are 7,37. Prime factorization of 259 in exponential form is:
259 = 71×371
Now multiplying the highest exponent prime factors to calculate the LCM of 255 and 259.
LCM(255,259) = 31×51×71×171×371
LCM(255,259) = 66045
Factors of 255
List of positive integer factors of 255 that divides 255 without a remainder.
1, 3, 5, 15, 17, 51, 85, 255
Factors of 259
List of positive integer factors of 259 that divides 259 without a remainder.
1, 7, 37, 259
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 255 and 259, than apply into the LCM equation.
GCF(255,259) = 1
LCM(255,259) = ( 255 × 259) / 1
LCM(255,259) = 66045 / 1
LCM(255,259) = 66045
(i) The LCM of 259 and 255 is associative
LCM of 255 and 259 = LCM of 259 and 255
1. What is the LCM of 255 and 259?
Answer: LCM of 255 and 259 is 66045.
2. What are the Factors of 255?
Answer: Factors of 255 are 1, 3, 5, 15, 17, 51, 85, 255. There are 8 integers that are factors of 255. The greatest factor of 255 is 255.
3. What are the Factors of 259?
Answer: Factors of 259 are 1, 7, 37, 259. There are 4 integers that are factors of 259. The greatest factor of 259 is 259.
4. How to Find the LCM of 255 and 259?
Answer:
Least Common Multiple of 255 and 259 = 66045
Step 1: Find the prime factorization of 255
255 = 3 x 5 x 17
Step 2: Find the prime factorization of 259
259 = 7 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 66045 = 3 x 5 x 7 x 17 x 37
Step 4: Therefore, the least common multiple of 255 and 259 is 66045.