Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8278 and 8282 the smallest integer that is 34279198 that is divisible by both numbers.
Least Common Multiple (LCM) of 8278 and 8282 is 34279198.
LCM(8278,8282) = 34279198
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 8278 and 8282. First we will calculate the prime factors of 8278 and 8282.
Prime Factorization of 8278
2 | 8278 |
4139 | 4139 |
1 |
Prime factors of 8278 are 2,4139. Prime factorization of 8278 in exponential form is:
8278 = 21×41391
Prime Factorization of 8282
2 | 8282 |
41 | 4141 |
101 | 101 |
1 |
Prime factors of 8282 are 2, 41,101. Prime factorization of 8282 in exponential form is:
8282 = 21×411×1011
Now multiplying the highest exponent prime factors to calculate the LCM of 8278 and 8282.
LCM(8278,8282) = 21×411×1011×41391
LCM(8278,8282) = 34279198
Factors of 8278
List of positive integer factors of 8278 that divides 8278 without a remainder.
1, 2, 4139, 8278
Factors of 8282
List of positive integer factors of 8282 that divides 8282 without a remainder.
1, 2, 41, 82, 101, 202, 4141, 8282
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8278 and 8282, than apply into the LCM equation.
GCF(8278,8282) = 2
LCM(8278,8282) = ( 8278 × 8282) / 2
LCM(8278,8282) = 68558396 / 2
LCM(8278,8282) = 34279198
(i) The LCM of 8282 and 8278 is associative
LCM of 8278 and 8282 = LCM of 8282 and 8278
1. What is the LCM of 8278 and 8282?
Answer: LCM of 8278 and 8282 is 34279198.
2. What are the Factors of 8278?
Answer: Factors of 8278 are 1, 2, 4139, 8278. There are 4 integers that are factors of 8278. The greatest factor of 8278 is 8278.
3. What are the Factors of 8282?
Answer: Factors of 8282 are 1, 2, 41, 82, 101, 202, 4141, 8282. There are 8 integers that are factors of 8282. The greatest factor of 8282 is 8282.
4. How to Find the LCM of 8278 and 8282?
Answer:
Least Common Multiple of 8278 and 8282 = 34279198
Step 1: Find the prime factorization of 8278
8278 = 2 x 4139
Step 2: Find the prime factorization of 8282
8282 = 2 x 41 x 101
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 34279198 = 2 x 41 x 101 x 4139
Step 4: Therefore, the least common multiple of 8278 and 8282 is 34279198.