Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1512 and 1517 the smallest integer that is 2293704 that is divisible by both numbers.
Least Common Multiple (LCM) of 1512 and 1517 is 2293704.
LCM(1512,1517) = 2293704
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 1512 and 1517. First we will calculate the prime factors of 1512 and 1517.
Prime Factorization of 1512
2 | 1512 |
2 | 756 |
2 | 378 |
3 | 189 |
3 | 63 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 1512 are 2, 3,7. Prime factorization of 1512 in exponential form is:
1512 = 23×33×71
Prime Factorization of 1517
37 | 1517 |
41 | 41 |
1 |
Prime factors of 1517 are 37,41. Prime factorization of 1517 in exponential form is:
1517 = 371×411
Now multiplying the highest exponent prime factors to calculate the LCM of 1512 and 1517.
LCM(1512,1517) = 23×33×71×371×411
LCM(1512,1517) = 2293704
Factors of 1512
List of positive integer factors of 1512 that divides 1512 without a remainder.
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512
Factors of 1517
List of positive integer factors of 1517 that divides 1517 without a remainder.
1, 37, 41, 1517
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1512 and 1517, than apply into the LCM equation.
GCF(1512,1517) = 1
LCM(1512,1517) = ( 1512 × 1517) / 1
LCM(1512,1517) = 2293704 / 1
LCM(1512,1517) = 2293704
(i) The LCM of 1517 and 1512 is associative
LCM of 1512 and 1517 = LCM of 1517 and 1512
1. What is the LCM of 1512 and 1517?
Answer: LCM of 1512 and 1517 is 2293704.
2. What are the Factors of 1512?
Answer: Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512. There are 32 integers that are factors of 1512. The greatest factor of 1512 is 1512.
3. What are the Factors of 1517?
Answer: Factors of 1517 are 1, 37, 41, 1517. There are 4 integers that are factors of 1517. The greatest factor of 1517 is 1517.
4. How to Find the LCM of 1512 and 1517?
Answer:
Least Common Multiple of 1512 and 1517 = 2293704
Step 1: Find the prime factorization of 1512
1512 = 2 x 2 x 2 x 3 x 3 x 3 x 7
Step 2: Find the prime factorization of 1517
1517 = 37 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2293704 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 37 x 41
Step 4: Therefore, the least common multiple of 1512 and 1517 is 2293704.