Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1020 and 1027 the smallest integer that is 1047540 that is divisible by both numbers.
Least Common Multiple (LCM) of 1020 and 1027 is 1047540.
LCM(1020,1027) = 1047540
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 1020 and 1027. First we will calculate the prime factors of 1020 and 1027.
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
Prime Factorization of 1027
13 | 1027 |
79 | 79 |
1 |
Prime factors of 1027 are 13,79. Prime factorization of 1027 in exponential form is:
1027 = 131×791
Now multiplying the highest exponent prime factors to calculate the LCM of 1020 and 1027.
LCM(1020,1027) = 22×31×51×131×171×791
LCM(1020,1027) = 1047540
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
Factors of 1027
List of positive integer factors of 1027 that divides 1027 without a remainder.
1, 13, 79, 1027
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1020 and 1027, than apply into the LCM equation.
GCF(1020,1027) = 1
LCM(1020,1027) = ( 1020 × 1027) / 1
LCM(1020,1027) = 1047540 / 1
LCM(1020,1027) = 1047540
(i) The LCM of 1027 and 1020 is associative
LCM of 1020 and 1027 = LCM of 1027 and 1020
1. What is the LCM of 1020 and 1027?
Answer: LCM of 1020 and 1027 is 1047540.
2. 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.
3. What are the Factors of 1027?
Answer: Factors of 1027 are 1, 13, 79, 1027. There are 4 integers that are factors of 1027. The greatest factor of 1027 is 1027.
4. How to Find the LCM of 1020 and 1027?
Answer:
Least Common Multiple of 1020 and 1027 = 1047540
Step 1: Find the prime factorization of 1020
1020 = 2 x 2 x 3 x 5 x 17
Step 2: Find the prime factorization of 1027
1027 = 13 x 79
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1047540 = 2 x 2 x 3 x 5 x 13 x 17 x 79
Step 4: Therefore, the least common multiple of 1020 and 1027 is 1047540.