Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10010 and 10017 the smallest integer that is 14324310 that is divisible by both numbers.
Least Common Multiple (LCM) of 10010 and 10017 is 14324310.
LCM(10010,10017) = 14324310
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 10010 and 10017. First we will calculate the prime factors of 10010 and 10017.
Prime Factorization of 10010
2 | 10010 |
5 | 5005 |
7 | 1001 |
11 | 143 |
13 | 13 |
1 |
Prime factors of 10010 are 2, 5, 7, 11,13. Prime factorization of 10010 in exponential form is:
10010 = 21×51×71×111×131
Prime Factorization of 10017
3 | 10017 |
3 | 3339 |
3 | 1113 |
7 | 371 |
53 | 53 |
1 |
Prime factors of 10017 are 3, 7,53. Prime factorization of 10017 in exponential form is:
10017 = 33×71×531
Now multiplying the highest exponent prime factors to calculate the LCM of 10010 and 10017.
LCM(10010,10017) = 21×33×51×71×111×131×531
LCM(10010,10017) = 14324310
Factors of 10010
List of positive integer factors of 10010 that divides 10010 without a remainder.
1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010
Factors of 10017
List of positive integer factors of 10017 that divides 10017 without a remainder.
1, 3, 7, 9, 21, 27, 53, 63, 159, 189, 371, 477, 1113, 1431, 3339, 10017
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10010 and 10017, than apply into the LCM equation.
GCF(10010,10017) = 7
LCM(10010,10017) = ( 10010 × 10017) / 7
LCM(10010,10017) = 100270170 / 7
LCM(10010,10017) = 14324310
(i) The LCM of 10017 and 10010 is associative
LCM of 10010 and 10017 = LCM of 10017 and 10010
1. What is the LCM of 10010 and 10017?
Answer: LCM of 10010 and 10017 is 14324310.
2. What are the Factors of 10010?
Answer: Factors of 10010 are 1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010. There are 32 integers that are factors of 10010. The greatest factor of 10010 is 10010.
3. What are the Factors of 10017?
Answer: Factors of 10017 are 1, 3, 7, 9, 21, 27, 53, 63, 159, 189, 371, 477, 1113, 1431, 3339, 10017. There are 16 integers that are factors of 10017. The greatest factor of 10017 is 10017.
4. How to Find the LCM of 10010 and 10017?
Answer:
Least Common Multiple of 10010 and 10017 = 14324310
Step 1: Find the prime factorization of 10010
10010 = 2 x 5 x 7 x 11 x 13
Step 2: Find the prime factorization of 10017
10017 = 3 x 3 x 3 x 7 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14324310 = 2 x 3 x 3 x 3 x 5 x 7 x 11 x 13 x 53
Step 4: Therefore, the least common multiple of 10010 and 10017 is 14324310.