Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 63 and 82 the smallest integer that is 5166 that is divisible by both numbers.
Least Common Multiple (LCM) of 63 and 82 is 5166.
LCM(63,82) = 5166
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 63 and 82. First we will calculate the prime factors of 63 and 82.
Prime Factorization of 63
3 | 63 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:
63 = 32×71
Prime Factorization of 82
2 | 82 |
41 | 41 |
1 |
Prime factors of 82 are 2,41. Prime factorization of 82 in exponential form is:
82 = 21×411
Now multiplying the highest exponent prime factors to calculate the LCM of 63 and 82.
LCM(63,82) = 21×32×71×411
LCM(63,82) = 5166
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1, 3, 7, 9, 21, 63
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1, 2, 41, 82
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 63 and 82, than apply into the LCM equation.
GCF(63,82) = 1
LCM(63,82) = ( 63 × 82) / 1
LCM(63,82) = 5166 / 1
LCM(63,82) = 5166
(i) The LCM of 82 and 63 is associative
LCM of 63 and 82 = LCM of 82 and 63
1. What is the LCM of 63 and 82?
Answer: LCM of 63 and 82 is 5166.
2. What are the Factors of 63?
Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.
3. What are the Factors of 82?
Answer: Factors of 82 are 1, 2, 41, 82. There are 4 integers that are factors of 82. The greatest factor of 82 is 82.
4. How to Find the LCM of 63 and 82?
Answer:
Least Common Multiple of 63 and 82 = 5166
Step 1: Find the prime factorization of 63
63 = 3 x 3 x 7
Step 2: Find the prime factorization of 82
82 = 2 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5166 = 2 x 3 x 3 x 7 x 41
Step 4: Therefore, the least common multiple of 63 and 82 is 5166.