Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8375 and 8382 the smallest integer that is 70199250 that is divisible by both numbers.
Least Common Multiple (LCM) of 8375 and 8382 is 70199250.
LCM(8375,8382) = 70199250
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 8375 and 8382. First we will calculate the prime factors of 8375 and 8382.
Prime Factorization of 8375
5 | 8375 |
5 | 1675 |
5 | 335 |
67 | 67 |
1 |
Prime factors of 8375 are 5,67. Prime factorization of 8375 in exponential form is:
8375 = 53×671
Prime Factorization of 8382
2 | 8382 |
3 | 4191 |
11 | 1397 |
127 | 127 |
1 |
Prime factors of 8382 are 2, 3, 11,127. Prime factorization of 8382 in exponential form is:
8382 = 21×31×111×1271
Now multiplying the highest exponent prime factors to calculate the LCM of 8375 and 8382.
LCM(8375,8382) = 21×31×53×111×671×1271
LCM(8375,8382) = 70199250
Factors of 8375
List of positive integer factors of 8375 that divides 8375 without a remainder.
1, 5, 25, 67, 125, 335, 1675, 8375
Factors of 8382
List of positive integer factors of 8382 that divides 8382 without a remainder.
1, 2, 3, 6, 11, 22, 33, 66, 127, 254, 381, 762, 1397, 2794, 4191, 8382
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8375 and 8382, than apply into the LCM equation.
GCF(8375,8382) = 1
LCM(8375,8382) = ( 8375 × 8382) / 1
LCM(8375,8382) = 70199250 / 1
LCM(8375,8382) = 70199250
(i) The LCM of 8382 and 8375 is associative
LCM of 8375 and 8382 = LCM of 8382 and 8375
1. What is the LCM of 8375 and 8382?
Answer: LCM of 8375 and 8382 is 70199250.
2. What are the Factors of 8375?
Answer: Factors of 8375 are 1, 5, 25, 67, 125, 335, 1675, 8375. There are 8 integers that are factors of 8375. The greatest factor of 8375 is 8375.
3. What are the Factors of 8382?
Answer: Factors of 8382 are 1, 2, 3, 6, 11, 22, 33, 66, 127, 254, 381, 762, 1397, 2794, 4191, 8382. There are 16 integers that are factors of 8382. The greatest factor of 8382 is 8382.
4. How to Find the LCM of 8375 and 8382?
Answer:
Least Common Multiple of 8375 and 8382 = 70199250
Step 1: Find the prime factorization of 8375
8375 = 5 x 5 x 5 x 67
Step 2: Find the prime factorization of 8382
8382 = 2 x 3 x 11 x 127
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 70199250 = 2 x 3 x 5 x 5 x 5 x 11 x 67 x 127
Step 4: Therefore, the least common multiple of 8375 and 8382 is 70199250.