Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 462 and 466 the smallest integer that is 107646 that is divisible by both numbers.
Least Common Multiple (LCM) of 462 and 466 is 107646.
LCM(462,466) = 107646
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 462 and 466. First we will calculate the prime factors of 462 and 466.
Prime Factorization of 462
2 | 462 |
3 | 231 |
7 | 77 |
11 | 11 |
1 |
Prime factors of 462 are 2, 3, 7,11. Prime factorization of 462 in exponential form is:
462 = 21×31×71×111
Prime Factorization of 466
2 | 466 |
233 | 233 |
1 |
Prime factors of 466 are 2,233. Prime factorization of 466 in exponential form is:
466 = 21×2331
Now multiplying the highest exponent prime factors to calculate the LCM of 462 and 466.
LCM(462,466) = 21×31×71×111×2331
LCM(462,466) = 107646
Factors of 462
List of positive integer factors of 462 that divides 462 without a remainder.
1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
Factors of 466
List of positive integer factors of 466 that divides 466 without a remainder.
1, 2, 233, 466
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 462 and 466, than apply into the LCM equation.
GCF(462,466) = 2
LCM(462,466) = ( 462 × 466) / 2
LCM(462,466) = 215292 / 2
LCM(462,466) = 107646
(i) The LCM of 466 and 462 is associative
LCM of 462 and 466 = LCM of 466 and 462
1. What is the LCM of 462 and 466?
Answer: LCM of 462 and 466 is 107646.
2. What are the Factors of 462?
Answer: Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462. There are 16 integers that are factors of 462. The greatest factor of 462 is 462.
3. What are the Factors of 466?
Answer: Factors of 466 are 1, 2, 233, 466. There are 4 integers that are factors of 466. The greatest factor of 466 is 466.
4. How to Find the LCM of 462 and 466?
Answer:
Least Common Multiple of 462 and 466 = 107646
Step 1: Find the prime factorization of 462
462 = 2 x 3 x 7 x 11
Step 2: Find the prime factorization of 466
466 = 2 x 233
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 107646 = 2 x 3 x 7 x 11 x 233
Step 4: Therefore, the least common multiple of 462 and 466 is 107646.