Least Common Multiple of 82 and 87
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 82 and 87 the smallest integer that is 7134 that is divisible by both numbers.
Least Common Multiple (LCM) of 82 and 87 is 7134.
LCM(82,87) = 7134
LCM of 82 and 87
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 82 and 87 by Prime method
- Least Common Multiple of 82 and 87 with GCF Formula
LCM of 82 and 87 is 7134
Least common multiple can be found by multiplying the highest exponent prime factors of 82 and 87. First we will calculate the prime factors of 82 and 87.
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
Prime Factorization of 87
| 3 | 87 |
| 29 | 29 |
| 1 |
Prime factors of 87 are 3,29. Prime factorization of 87 in exponential form is:
87 = 31×291
Now multiplying the highest exponent prime factors to calculate the LCM of 82 and 87.
LCM(82,87) = 21×31×291×411
LCM(82,87) = 7134
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1, 2, 41, 82
Factors of 87
List of positive integer factors of 87 that divides 87 without a remainder.
1, 3, 29, 87
Least Common Multiple of 82 and 87 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82 and 87, than apply into the LCM equation.
GCF(82,87) = 1
LCM(82,87) = ( 82 × 87) / 1
LCM(82,87) = 7134 / 1
LCM(82,87) = 7134
Properties of LCM 82 and 87
(i) The LCM of 87 and 82 is associative
LCM of 82 and 87 = LCM of 87 and 82
Related Least Common Multiples of 82
Related Least Common Multiples of 87
Frequently Asked Questions on LCM of 82 and 87
1. What is the LCM of 82 and 87?
Answer: LCM of 82 and 87 is 7134.
2. 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.
3. What are the Factors of 87?
Answer: Factors of 87 are 1, 3, 29, 87. There are 4 integers that are factors of 87. The greatest factor of 87 is 87.
4. How to Find the LCM of 82 and 87?
Answer:
Least Common Multiple of 82 and 87 = 7134
Step 1: Find the prime factorization of 82
82 = 2 x 41
Step 2: Find the prime factorization of 87
87 = 3 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7134 = 2 x 3 x 29 x 41
Step 4: Therefore, the least common multiple of 82 and 87 is 7134.