Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 254 and 257 the smallest integer that is 65278 that is divisible by both numbers.
Least Common Multiple (LCM) of 254 and 257 is 65278.
LCM(254,257) = 65278
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 254 and 257. First we will calculate the prime factors of 254 and 257.
Prime Factorization of 254
2 | 254 |
127 | 127 |
1 |
Prime factors of 254 are 2,127. Prime factorization of 254 in exponential form is:
254 = 21×1271
Prime Factorization of 257
257 | 257 |
1 |
Prime factors of 257 are 257. Prime factorization of 257 in exponential form is:
257 = 2571
Now multiplying the highest exponent prime factors to calculate the LCM of 254 and 257.
LCM(254,257) = 21×1271×2571
LCM(254,257) = 65278
Factors of 254
List of positive integer factors of 254 that divides 254 without a remainder.
1, 2, 127, 254
Factors of 257
List of positive integer factors of 257 that divides 257 without a remainder.
1, 257
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 254 and 257, than apply into the LCM equation.
GCF(254,257) = 1
LCM(254,257) = ( 254 × 257) / 1
LCM(254,257) = 65278 / 1
LCM(254,257) = 65278
(i) The LCM of 257 and 254 is associative
LCM of 254 and 257 = LCM of 257 and 254
1. What is the LCM of 254 and 257?
Answer: LCM of 254 and 257 is 65278.
2. What are the Factors of 254?
Answer: Factors of 254 are 1, 2, 127, 254. There are 4 integers that are factors of 254. The greatest factor of 254 is 254.
3. What are the Factors of 257?
Answer: Factors of 257 are 1, 257. There are 2 integers that are factors of 257. The greatest factor of 257 is 257.
4. How to Find the LCM of 254 and 257?
Answer:
Least Common Multiple of 254 and 257 = 65278
Step 1: Find the prime factorization of 254
254 = 2 x 127
Step 2: Find the prime factorization of 257
257 = 257
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 65278 = 2 x 127 x 257
Step 4: Therefore, the least common multiple of 254 and 257 is 65278.