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 262 the smallest integer that is 66810 that is divisible by both numbers.
Least Common Multiple (LCM) of 255 and 262 is 66810.
LCM(255,262) = 66810
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 262. First we will calculate the prime factors of 255 and 262.
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 262
2 | 262 |
131 | 131 |
1 |
Prime factors of 262 are 2,131. Prime factorization of 262 in exponential form is:
262 = 21×1311
Now multiplying the highest exponent prime factors to calculate the LCM of 255 and 262.
LCM(255,262) = 21×31×51×171×1311
LCM(255,262) = 66810
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 262
List of positive integer factors of 262 that divides 262 without a remainder.
1, 2, 131, 262
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 255 and 262, than apply into the LCM equation.
GCF(255,262) = 1
LCM(255,262) = ( 255 × 262) / 1
LCM(255,262) = 66810 / 1
LCM(255,262) = 66810
(i) The LCM of 262 and 255 is associative
LCM of 255 and 262 = LCM of 262 and 255
1. What is the LCM of 255 and 262?
Answer: LCM of 255 and 262 is 66810.
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 262?
Answer: Factors of 262 are 1, 2, 131, 262. There are 4 integers that are factors of 262. The greatest factor of 262 is 262.
4. How to Find the LCM of 255 and 262?
Answer:
Least Common Multiple of 255 and 262 = 66810
Step 1: Find the prime factorization of 255
255 = 3 x 5 x 17
Step 2: Find the prime factorization of 262
262 = 2 x 131
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 66810 = 2 x 3 x 5 x 17 x 131
Step 4: Therefore, the least common multiple of 255 and 262 is 66810.