Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9003 and 9010 the smallest integer that is 81117030 that is divisible by both numbers.
Least Common Multiple (LCM) of 9003 and 9010 is 81117030.
LCM(9003,9010) = 81117030
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 9003 and 9010. First we will calculate the prime factors of 9003 and 9010.
Prime Factorization of 9003
3 | 9003 |
3001 | 3001 |
1 |
Prime factors of 9003 are 3,3001. Prime factorization of 9003 in exponential form is:
9003 = 31×30011
Prime Factorization of 9010
2 | 9010 |
5 | 4505 |
17 | 901 |
53 | 53 |
1 |
Prime factors of 9010 are 2, 5, 17,53. Prime factorization of 9010 in exponential form is:
9010 = 21×51×171×531
Now multiplying the highest exponent prime factors to calculate the LCM of 9003 and 9010.
LCM(9003,9010) = 21×31×51×171×531×30011
LCM(9003,9010) = 81117030
Factors of 9003
List of positive integer factors of 9003 that divides 9003 without a remainder.
1, 3, 3001, 9003
Factors of 9010
List of positive integer factors of 9010 that divides 9010 without a remainder.
1, 2, 5, 10, 17, 34, 53, 85, 106, 170, 265, 530, 901, 1802, 4505, 9010
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9003 and 9010, than apply into the LCM equation.
GCF(9003,9010) = 1
LCM(9003,9010) = ( 9003 × 9010) / 1
LCM(9003,9010) = 81117030 / 1
LCM(9003,9010) = 81117030
(i) The LCM of 9010 and 9003 is associative
LCM of 9003 and 9010 = LCM of 9010 and 9003
1. What is the LCM of 9003 and 9010?
Answer: LCM of 9003 and 9010 is 81117030.
2. What are the Factors of 9003?
Answer: Factors of 9003 are 1, 3, 3001, 9003. There are 4 integers that are factors of 9003. The greatest factor of 9003 is 9003.
3. What are the Factors of 9010?
Answer: Factors of 9010 are 1, 2, 5, 10, 17, 34, 53, 85, 106, 170, 265, 530, 901, 1802, 4505, 9010. There are 16 integers that are factors of 9010. The greatest factor of 9010 is 9010.
4. How to Find the LCM of 9003 and 9010?
Answer:
Least Common Multiple of 9003 and 9010 = 81117030
Step 1: Find the prime factorization of 9003
9003 = 3 x 3001
Step 2: Find the prime factorization of 9010
9010 = 2 x 5 x 17 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 = 81117030 = 2 x 3 x 5 x 17 x 53 x 3001
Step 4: Therefore, the least common multiple of 9003 and 9010 is 81117030.