Least Common Multiple of 82 and 90
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 90 the smallest integer that is 3690 that is divisible by both numbers.
Least Common Multiple (LCM) of 82 and 90 is 3690.
LCM(82,90) = 3690
LCM of 82 and 90
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 82 and 90 by Prime method
- Least Common Multiple of 82 and 90 with GCF Formula
LCM of 82 and 90 is 3690
Least common multiple can be found by multiplying the highest exponent prime factors of 82 and 90. First we will calculate the prime factors of 82 and 90.
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 90
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 90 are 2, 3,5. Prime factorization of 90 in exponential form is:
90 = 21×32×51
Now multiplying the highest exponent prime factors to calculate the LCM of 82 and 90.
LCM(82,90) = 21×32×51×411
LCM(82,90) = 3690
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1, 2, 41, 82
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Least Common Multiple of 82 and 90 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 90, than apply into the LCM equation.
GCF(82,90) = 2
LCM(82,90) = ( 82 × 90) / 2
LCM(82,90) = 7380 / 2
LCM(82,90) = 3690
Properties of LCM 82 and 90
(i) The LCM of 90 and 82 is associative
LCM of 82 and 90 = LCM of 90 and 82
Related Least Common Multiples of 82
Related Least Common Multiples of 90
Frequently Asked Questions on LCM of 82 and 90
1. What is the LCM of 82 and 90?
Answer: LCM of 82 and 90 is 3690.
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 90?
Answer: Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. There are 12 integers that are factors of 90. The greatest factor of 90 is 90.
4. How to Find the LCM of 82 and 90?
Answer:
Least Common Multiple of 82 and 90 = 3690
Step 1: Find the prime factorization of 82
82 = 2 x 41
Step 2: Find the prime factorization of 90
90 = 2 x 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3690 = 2 x 3 x 3 x 5 x 41
Step 4: Therefore, the least common multiple of 82 and 90 is 3690.