Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 265 and 269 the smallest integer that is 71285 that is divisible by both numbers.
Least Common Multiple (LCM) of 265 and 269 is 71285.
LCM(265,269) = 71285
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 265 and 269. First we will calculate the prime factors of 265 and 269.
Prime Factorization of 265
5 | 265 |
53 | 53 |
1 |
Prime factors of 265 are 5,53. Prime factorization of 265 in exponential form is:
265 = 51×531
Prime Factorization of 269
269 | 269 |
1 |
Prime factors of 269 are 269. Prime factorization of 269 in exponential form is:
269 = 2691
Now multiplying the highest exponent prime factors to calculate the LCM of 265 and 269.
LCM(265,269) = 51×531×2691
LCM(265,269) = 71285
Factors of 265
List of positive integer factors of 265 that divides 265 without a remainder.
1, 5, 53, 265
Factors of 269
List of positive integer factors of 269 that divides 269 without a remainder.
1, 269
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 265 and 269, than apply into the LCM equation.
GCF(265,269) = 1
LCM(265,269) = ( 265 × 269) / 1
LCM(265,269) = 71285 / 1
LCM(265,269) = 71285
(i) The LCM of 269 and 265 is associative
LCM of 265 and 269 = LCM of 269 and 265
1. What is the LCM of 265 and 269?
Answer: LCM of 265 and 269 is 71285.
2. What are the Factors of 265?
Answer: Factors of 265 are 1, 5, 53, 265. There are 4 integers that are factors of 265. The greatest factor of 265 is 265.
3. What are the Factors of 269?
Answer: Factors of 269 are 1, 269. There are 2 integers that are factors of 269. The greatest factor of 269 is 269.
4. How to Find the LCM of 265 and 269?
Answer:
Least Common Multiple of 265 and 269 = 71285
Step 1: Find the prime factorization of 265
265 = 5 x 53
Step 2: Find the prime factorization of 269
269 = 269
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 71285 = 5 x 53 x 269
Step 4: Therefore, the least common multiple of 265 and 269 is 71285.