Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8514 and 8522 the smallest integer that is 36278154 that is divisible by both numbers.
Least Common Multiple (LCM) of 8514 and 8522 is 36278154.
LCM(8514,8522) = 36278154
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 8514 and 8522. First we will calculate the prime factors of 8514 and 8522.
Prime Factorization of 8514
2 | 8514 |
3 | 4257 |
3 | 1419 |
11 | 473 |
43 | 43 |
1 |
Prime factors of 8514 are 2, 3, 11,43. Prime factorization of 8514 in exponential form is:
8514 = 21×32×111×431
Prime Factorization of 8522
2 | 8522 |
4261 | 4261 |
1 |
Prime factors of 8522 are 2,4261. Prime factorization of 8522 in exponential form is:
8522 = 21×42611
Now multiplying the highest exponent prime factors to calculate the LCM of 8514 and 8522.
LCM(8514,8522) = 21×32×111×431×42611
LCM(8514,8522) = 36278154
Factors of 8514
List of positive integer factors of 8514 that divides 8514 without a remainder.
1, 2, 3, 6, 9, 11, 18, 22, 33, 43, 66, 86, 99, 129, 198, 258, 387, 473, 774, 946, 1419, 2838, 4257, 8514
Factors of 8522
List of positive integer factors of 8522 that divides 8522 without a remainder.
1, 2, 4261, 8522
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8514 and 8522, than apply into the LCM equation.
GCF(8514,8522) = 2
LCM(8514,8522) = ( 8514 × 8522) / 2
LCM(8514,8522) = 72556308 / 2
LCM(8514,8522) = 36278154
(i) The LCM of 8522 and 8514 is associative
LCM of 8514 and 8522 = LCM of 8522 and 8514
1. What is the LCM of 8514 and 8522?
Answer: LCM of 8514 and 8522 is 36278154.
2. What are the Factors of 8514?
Answer: Factors of 8514 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 43, 66, 86, 99, 129, 198, 258, 387, 473, 774, 946, 1419, 2838, 4257, 8514. There are 24 integers that are factors of 8514. The greatest factor of 8514 is 8514.
3. What are the Factors of 8522?
Answer: Factors of 8522 are 1, 2, 4261, 8522. There are 4 integers that are factors of 8522. The greatest factor of 8522 is 8522.
4. How to Find the LCM of 8514 and 8522?
Answer:
Least Common Multiple of 8514 and 8522 = 36278154
Step 1: Find the prime factorization of 8514
8514 = 2 x 3 x 3 x 11 x 43
Step 2: Find the prime factorization of 8522
8522 = 2 x 4261
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 36278154 = 2 x 3 x 3 x 11 x 43 x 4261
Step 4: Therefore, the least common multiple of 8514 and 8522 is 36278154.