Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 40010 and 40016 the smallest integer that is 800520080 that is divisible by both numbers.
Least Common Multiple (LCM) of 40010 and 40016 is 800520080.
LCM(40010,40016) = 800520080
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 40010 and 40016. First we will calculate the prime factors of 40010 and 40016.
Prime Factorization of 40010
2 | 40010 |
5 | 20005 |
4001 | 4001 |
1 |
Prime factors of 40010 are 2, 5,4001. Prime factorization of 40010 in exponential form is:
40010 = 21×51×40011
Prime Factorization of 40016
2 | 40016 |
2 | 20008 |
2 | 10004 |
2 | 5002 |
41 | 2501 |
61 | 61 |
1 |
Prime factors of 40016 are 2, 41,61. Prime factorization of 40016 in exponential form is:
40016 = 24×411×611
Now multiplying the highest exponent prime factors to calculate the LCM of 40010 and 40016.
LCM(40010,40016) = 24×51×411×611×40011
LCM(40010,40016) = 800520080
Factors of 40010
List of positive integer factors of 40010 that divides 40010 without a remainder.
1, 2, 5, 10, 4001, 8002, 20005, 40010
Factors of 40016
List of positive integer factors of 40016 that divides 40016 without a remainder.
1, 2, 4, 8, 16, 41, 61, 82, 122, 164, 244, 328, 488, 656, 976, 2501, 5002, 10004, 20008, 40016
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40010 and 40016, than apply into the LCM equation.
GCF(40010,40016) = 2
LCM(40010,40016) = ( 40010 × 40016) / 2
LCM(40010,40016) = 1601040160 / 2
LCM(40010,40016) = 800520080
(i) The LCM of 40016 and 40010 is associative
LCM of 40010 and 40016 = LCM of 40016 and 40010
1. What is the LCM of 40010 and 40016?
Answer: LCM of 40010 and 40016 is 800520080.
2. What are the Factors of 40010?
Answer: Factors of 40010 are 1, 2, 5, 10, 4001, 8002, 20005, 40010. There are 8 integers that are factors of 40010. The greatest factor of 40010 is 40010.
3. What are the Factors of 40016?
Answer: Factors of 40016 are 1, 2, 4, 8, 16, 41, 61, 82, 122, 164, 244, 328, 488, 656, 976, 2501, 5002, 10004, 20008, 40016. There are 20 integers that are factors of 40016. The greatest factor of 40016 is 40016.
4. How to Find the LCM of 40010 and 40016?
Answer:
Least Common Multiple of 40010 and 40016 = 800520080
Step 1: Find the prime factorization of 40010
40010 = 2 x 5 x 4001
Step 2: Find the prime factorization of 40016
40016 = 2 x 2 x 2 x 2 x 41 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 800520080 = 2 x 2 x 2 x 2 x 5 x 41 x 61 x 4001
Step 4: Therefore, the least common multiple of 40010 and 40016 is 800520080.