Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1015 and 1020 the smallest integer that is 207060 that is divisible by both numbers.
Least Common Multiple (LCM) of 1015 and 1020 is 207060.
LCM(1015,1020) = 207060
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 1015 and 1020. First we will calculate the prime factors of 1015 and 1020.
Prime Factorization of 1015
5 | 1015 |
7 | 203 |
29 | 29 |
1 |
Prime factors of 1015 are 5, 7,29. Prime factorization of 1015 in exponential form is:
1015 = 51×71×291
Prime Factorization of 1020
2 | 1020 |
2 | 510 |
3 | 255 |
5 | 85 |
17 | 17 |
1 |
Prime factors of 1020 are 2, 3, 5,17. Prime factorization of 1020 in exponential form is:
1020 = 22×31×51×171
Now multiplying the highest exponent prime factors to calculate the LCM of 1015 and 1020.
LCM(1015,1020) = 22×31×51×71×171×291
LCM(1015,1020) = 207060
Factors of 1015
List of positive integer factors of 1015 that divides 1015 without a remainder.
1, 5, 7, 29, 35, 145, 203, 1015
Factors of 1020
List of positive integer factors of 1020 that divides 1020 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, 1020
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1015 and 1020, than apply into the LCM equation.
GCF(1015,1020) = 5
LCM(1015,1020) = ( 1015 × 1020) / 5
LCM(1015,1020) = 1035300 / 5
LCM(1015,1020) = 207060
(i) The LCM of 1020 and 1015 is associative
LCM of 1015 and 1020 = LCM of 1020 and 1015
1. What is the LCM of 1015 and 1020?
Answer: LCM of 1015 and 1020 is 207060.
2. What are the Factors of 1015?
Answer: Factors of 1015 are 1, 5, 7, 29, 35, 145, 203, 1015. There are 8 integers that are factors of 1015. The greatest factor of 1015 is 1015.
3. What are the Factors of 1020?
Answer: Factors of 1020 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, 1020. There are 24 integers that are factors of 1020. The greatest factor of 1020 is 1020.
4. How to Find the LCM of 1015 and 1020?
Answer:
Least Common Multiple of 1015 and 1020 = 207060
Step 1: Find the prime factorization of 1015
1015 = 5 x 7 x 29
Step 2: Find the prime factorization of 1020
1020 = 2 x 2 x 3 x 5 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 207060 = 2 x 2 x 3 x 5 x 7 x 17 x 29
Step 4: Therefore, the least common multiple of 1015 and 1020 is 207060.