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 467 the smallest integer that is 214353 that is divisible by both numbers.
Least Common Multiple (LCM) of 459 and 467 is 214353.
LCM(459,467) = 214353
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 467. First we will calculate the prime factors of 459 and 467.
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 467
467 | 467 |
1 |
Prime factors of 467 are 467. Prime factorization of 467 in exponential form is:
467 = 4671
Now multiplying the highest exponent prime factors to calculate the LCM of 459 and 467.
LCM(459,467) = 33×171×4671
LCM(459,467) = 214353
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 467
List of positive integer factors of 467 that divides 467 without a remainder.
1, 467
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 459 and 467, than apply into the LCM equation.
GCF(459,467) = 1
LCM(459,467) = ( 459 × 467) / 1
LCM(459,467) = 214353 / 1
LCM(459,467) = 214353
(i) The LCM of 467 and 459 is associative
LCM of 459 and 467 = LCM of 467 and 459
1. What is the LCM of 459 and 467?
Answer: LCM of 459 and 467 is 214353.
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 467?
Answer: Factors of 467 are 1, 467. There are 2 integers that are factors of 467. The greatest factor of 467 is 467.
4. How to Find the LCM of 459 and 467?
Answer:
Least Common Multiple of 459 and 467 = 214353
Step 1: Find the prime factorization of 459
459 = 3 x 3 x 3 x 17
Step 2: Find the prime factorization of 467
467 = 467
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 214353 = 3 x 3 x 3 x 17 x 467
Step 4: Therefore, the least common multiple of 459 and 467 is 214353.