Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8427 and 8428 the smallest integer that is 71022756 that is divisible by both numbers.
Least Common Multiple (LCM) of 8427 and 8428 is 71022756.
LCM(8427,8428) = 71022756
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 8427 and 8428. First we will calculate the prime factors of 8427 and 8428.
Prime Factorization of 8427
3 | 8427 |
53 | 2809 |
53 | 53 |
1 |
Prime factors of 8427 are 3,53. Prime factorization of 8427 in exponential form is:
8427 = 31×532
Prime Factorization of 8428
2 | 8428 |
2 | 4214 |
7 | 2107 |
7 | 301 |
43 | 43 |
1 |
Prime factors of 8428 are 2, 7,43. Prime factorization of 8428 in exponential form is:
8428 = 22×72×431
Now multiplying the highest exponent prime factors to calculate the LCM of 8427 and 8428.
LCM(8427,8428) = 22×31×72×431×532
LCM(8427,8428) = 71022756
Factors of 8427
List of positive integer factors of 8427 that divides 8427 without a remainder.
1, 3, 53, 159, 2809, 8427
Factors of 8428
List of positive integer factors of 8428 that divides 8428 without a remainder.
1, 2, 4, 7, 14, 28, 43, 49, 86, 98, 172, 196, 301, 602, 1204, 2107, 4214, 8428
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8427 and 8428, than apply into the LCM equation.
GCF(8427,8428) = 1
LCM(8427,8428) = ( 8427 × 8428) / 1
LCM(8427,8428) = 71022756 / 1
LCM(8427,8428) = 71022756
(i) The LCM of 8428 and 8427 is associative
LCM of 8427 and 8428 = LCM of 8428 and 8427
1. What is the LCM of 8427 and 8428?
Answer: LCM of 8427 and 8428 is 71022756.
2. What are the Factors of 8427?
Answer: Factors of 8427 are 1, 3, 53, 159, 2809, 8427. There are 6 integers that are factors of 8427. The greatest factor of 8427 is 8427.
3. What are the Factors of 8428?
Answer: Factors of 8428 are 1, 2, 4, 7, 14, 28, 43, 49, 86, 98, 172, 196, 301, 602, 1204, 2107, 4214, 8428. There are 18 integers that are factors of 8428. The greatest factor of 8428 is 8428.
4. How to Find the LCM of 8427 and 8428?
Answer:
Least Common Multiple of 8427 and 8428 = 71022756
Step 1: Find the prime factorization of 8427
8427 = 3 x 53 x 53
Step 2: Find the prime factorization of 8428
8428 = 2 x 2 x 7 x 7 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 71022756 = 2 x 2 x 3 x 7 x 7 x 43 x 53 x 53
Step 4: Therefore, the least common multiple of 8427 and 8428 is 71022756.