Least Common Multiple of 78 and 82
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 78 and 82 the smallest integer that is 3198 that is divisible by both numbers.
Least Common Multiple (LCM) of 78 and 82 is 3198.
LCM(78,82) = 3198
LCM of 78 and 82
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 78 and 82 by Prime method
- Least Common Multiple of 78 and 82 with GCF Formula
LCM of 78 and 82 is 3198
Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 82. First we will calculate the prime factors of 78 and 82.
Prime Factorization of 78
| 2 | 78 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 78 are 2, 3,13. Prime factorization of 78 in exponential form is:
78 = 21×31×131
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 78 and 82.
LCM(78,82) = 21×31×131×411
LCM(78,82) = 3198
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1, 2, 3, 6, 13, 26, 39, 78
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1, 2, 41, 82
Least Common Multiple of 78 and 82 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78 and 82, than apply into the LCM equation.
GCF(78,82) = 2
LCM(78,82) = ( 78 × 82) / 2
LCM(78,82) = 6396 / 2
LCM(78,82) = 3198
Properties of LCM 78 and 82
(i) The LCM of 82 and 78 is associative
LCM of 78 and 82 = LCM of 82 and 78
Related Least Common Multiples of 78
Related Least Common Multiples of 82
Frequently Asked Questions on LCM of 78 and 82
1. What is the LCM of 78 and 82?
Answer: LCM of 78 and 82 is 3198.
2. What are the Factors of 78?
Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.
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 78 and 82?
Answer:
Least Common Multiple of 78 and 82 = 3198
Step 1: Find the prime factorization of 78
78 = 2 x 3 x 13
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 = 3198 = 2 x 3 x 13 x 41
Step 4: Therefore, the least common multiple of 78 and 82 is 3198.