Least Common Multiple of 75 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 75 and 82 the smallest integer that is 6150 that is divisible by both numbers.
Least Common Multiple (LCM) of 75 and 82 is 6150.
LCM(75,82) = 6150
LCM of 75 and 82
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 75 and 82 by Prime method
- Least Common Multiple of 75 and 82 with GCF Formula
LCM of 75 and 82 is 6150
Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 82. First we will calculate the prime factors of 75 and 82.
Prime Factorization of 75
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 75 are 3,5. Prime factorization of 75 in exponential form is:
75 = 31×52
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 75 and 82.
LCM(75,82) = 21×31×52×411
LCM(75,82) = 6150
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1, 3, 5, 15, 25, 75
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1, 2, 41, 82
Least Common Multiple of 75 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 75 and 82, than apply into the LCM equation.
GCF(75,82) = 1
LCM(75,82) = ( 75 × 82) / 1
LCM(75,82) = 6150 / 1
LCM(75,82) = 6150
Properties of LCM 75 and 82
(i) The LCM of 82 and 75 is associative
LCM of 75 and 82 = LCM of 82 and 75
Related Least Common Multiples of 75
Related Least Common Multiples of 82
Frequently Asked Questions on LCM of 75 and 82
1. What is the LCM of 75 and 82?
Answer: LCM of 75 and 82 is 6150.
2. What are the Factors of 75?
Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.
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 75 and 82?
Answer:
Least Common Multiple of 75 and 82 = 6150
Step 1: Find the prime factorization of 75
75 = 3 x 5 x 5
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 = 6150 = 2 x 3 x 5 x 5 x 41
Step 4: Therefore, the least common multiple of 75 and 82 is 6150.
