Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10012 and 10019 the smallest integer that is 100310228 that is divisible by both numbers.
Least Common Multiple (LCM) of 10012 and 10019 is 100310228.
LCM(10012,10019) = 100310228
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 10012 and 10019. First we will calculate the prime factors of 10012 and 10019.
Prime Factorization of 10012
2 | 10012 |
2 | 5006 |
2503 | 2503 |
1 |
Prime factors of 10012 are 2,2503. Prime factorization of 10012 in exponential form is:
10012 = 22×25031
Prime Factorization of 10019
43 | 10019 |
233 | 233 |
1 |
Prime factors of 10019 are 43,233. Prime factorization of 10019 in exponential form is:
10019 = 431×2331
Now multiplying the highest exponent prime factors to calculate the LCM of 10012 and 10019.
LCM(10012,10019) = 22×431×2331×25031
LCM(10012,10019) = 100310228
Factors of 10012
List of positive integer factors of 10012 that divides 10012 without a remainder.
1, 2, 4, 2503, 5006, 10012
Factors of 10019
List of positive integer factors of 10019 that divides 10019 without a remainder.
1, 43, 233, 10019
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10012 and 10019, than apply into the LCM equation.
GCF(10012,10019) = 1
LCM(10012,10019) = ( 10012 × 10019) / 1
LCM(10012,10019) = 100310228 / 1
LCM(10012,10019) = 100310228
(i) The LCM of 10019 and 10012 is associative
LCM of 10012 and 10019 = LCM of 10019 and 10012
1. What is the LCM of 10012 and 10019?
Answer: LCM of 10012 and 10019 is 100310228.
2. What are the Factors of 10012?
Answer: Factors of 10012 are 1, 2, 4, 2503, 5006, 10012. There are 6 integers that are factors of 10012. The greatest factor of 10012 is 10012.
3. What are the Factors of 10019?
Answer: Factors of 10019 are 1, 43, 233, 10019. There are 4 integers that are factors of 10019. The greatest factor of 10019 is 10019.
4. How to Find the LCM of 10012 and 10019?
Answer:
Least Common Multiple of 10012 and 10019 = 100310228
Step 1: Find the prime factorization of 10012
10012 = 2 x 2 x 2503
Step 2: Find the prime factorization of 10019
10019 = 43 x 233
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100310228 = 2 x 2 x 43 x 233 x 2503
Step 4: Therefore, the least common multiple of 10012 and 10019 is 100310228.