Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 459 and 460 the smallest integer that is 211140 that is divisible by both numbers.
Least Common Multiple (LCM) of 459 and 460 is 211140.
LCM(459,460) = 211140
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 459 and 460. First we will calculate the prime factors of 459 and 460.
Prime Factorization of 459
3 | 459 |
3 | 153 |
3 | 51 |
17 | 17 |
1 |
Prime factors of 459 are 3,17. Prime factorization of 459 in exponential form is:
459 = 33×171
Prime Factorization of 460
2 | 460 |
2 | 230 |
5 | 115 |
23 | 23 |
1 |
Prime factors of 460 are 2, 5,23. Prime factorization of 460 in exponential form is:
460 = 22×51×231
Now multiplying the highest exponent prime factors to calculate the LCM of 459 and 460.
LCM(459,460) = 22×33×51×171×231
LCM(459,460) = 211140
Factors of 459
List of positive integer factors of 459 that divides 459 without a remainder.
1, 3, 9, 17, 27, 51, 153, 459
Factors of 460
List of positive integer factors of 460 that divides 460 without a remainder.
1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 459 and 460, than apply into the LCM equation.
GCF(459,460) = 1
LCM(459,460) = ( 459 × 460) / 1
LCM(459,460) = 211140 / 1
LCM(459,460) = 211140
(i) The LCM of 460 and 459 is associative
LCM of 459 and 460 = LCM of 460 and 459
1. What is the LCM of 459 and 460?
Answer: LCM of 459 and 460 is 211140.
2. What are the Factors of 459?
Answer: Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459. There are 8 integers that are factors of 459. The greatest factor of 459 is 459.
3. What are the Factors of 460?
Answer: Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460. There are 12 integers that are factors of 460. The greatest factor of 460 is 460.
4. How to Find the LCM of 459 and 460?
Answer:
Least Common Multiple of 459 and 460 = 211140
Step 1: Find the prime factorization of 459
459 = 3 x 3 x 3 x 17
Step 2: Find the prime factorization of 460
460 = 2 x 2 x 5 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 211140 = 2 x 2 x 3 x 3 x 3 x 5 x 17 x 23
Step 4: Therefore, the least common multiple of 459 and 460 is 211140.