Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1014 and 1015 the smallest integer that is 1029210 that is divisible by both numbers.
Least Common Multiple (LCM) of 1014 and 1015 is 1029210.
LCM(1014,1015) = 1029210
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 1014 and 1015. First we will calculate the prime factors of 1014 and 1015.
Prime Factorization of 1014
2 | 1014 |
3 | 507 |
13 | 169 |
13 | 13 |
1 |
Prime factors of 1014 are 2, 3,13. Prime factorization of 1014 in exponential form is:
1014 = 21×31×132
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
Now multiplying the highest exponent prime factors to calculate the LCM of 1014 and 1015.
LCM(1014,1015) = 21×31×51×71×132×291
LCM(1014,1015) = 1029210
Factors of 1014
List of positive integer factors of 1014 that divides 1014 without a remainder.
1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014
Factors of 1015
List of positive integer factors of 1015 that divides 1015 without a remainder.
1, 5, 7, 29, 35, 145, 203, 1015
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1014 and 1015, than apply into the LCM equation.
GCF(1014,1015) = 1
LCM(1014,1015) = ( 1014 × 1015) / 1
LCM(1014,1015) = 1029210 / 1
LCM(1014,1015) = 1029210
(i) The LCM of 1015 and 1014 is associative
LCM of 1014 and 1015 = LCM of 1015 and 1014
1. What is the LCM of 1014 and 1015?
Answer: LCM of 1014 and 1015 is 1029210.
2. What are the Factors of 1014?
Answer: Factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014. There are 12 integers that are factors of 1014. The greatest factor of 1014 is 1014.
3. 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.
4. How to Find the LCM of 1014 and 1015?
Answer:
Least Common Multiple of 1014 and 1015 = 1029210
Step 1: Find the prime factorization of 1014
1014 = 2 x 3 x 13 x 13
Step 2: Find the prime factorization of 1015
1015 = 5 x 7 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1029210 = 2 x 3 x 5 x 7 x 13 x 13 x 29
Step 4: Therefore, the least common multiple of 1014 and 1015 is 1029210.