Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1513 and 1520 the smallest integer that is 2299760 that is divisible by both numbers.
Least Common Multiple (LCM) of 1513 and 1520 is 2299760.
LCM(1513,1520) = 2299760
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 1513 and 1520. First we will calculate the prime factors of 1513 and 1520.
Prime Factorization of 1513
17 | 1513 |
89 | 89 |
1 |
Prime factors of 1513 are 17,89. Prime factorization of 1513 in exponential form is:
1513 = 171×891
Prime Factorization of 1520
2 | 1520 |
2 | 760 |
2 | 380 |
2 | 190 |
5 | 95 |
19 | 19 |
1 |
Prime factors of 1520 are 2, 5,19. Prime factorization of 1520 in exponential form is:
1520 = 24×51×191
Now multiplying the highest exponent prime factors to calculate the LCM of 1513 and 1520.
LCM(1513,1520) = 24×51×171×191×891
LCM(1513,1520) = 2299760
Factors of 1513
List of positive integer factors of 1513 that divides 1513 without a remainder.
1, 17, 89, 1513
Factors of 1520
List of positive integer factors of 1520 that divides 1520 without a remainder.
1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1513 and 1520, than apply into the LCM equation.
GCF(1513,1520) = 1
LCM(1513,1520) = ( 1513 × 1520) / 1
LCM(1513,1520) = 2299760 / 1
LCM(1513,1520) = 2299760
(i) The LCM of 1520 and 1513 is associative
LCM of 1513 and 1520 = LCM of 1520 and 1513
1. What is the LCM of 1513 and 1520?
Answer: LCM of 1513 and 1520 is 2299760.
2. What are the Factors of 1513?
Answer: Factors of 1513 are 1, 17, 89, 1513. There are 4 integers that are factors of 1513. The greatest factor of 1513 is 1513.
3. What are the Factors of 1520?
Answer: Factors of 1520 are 1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520. There are 20 integers that are factors of 1520. The greatest factor of 1520 is 1520.
4. How to Find the LCM of 1513 and 1520?
Answer:
Least Common Multiple of 1513 and 1520 = 2299760
Step 1: Find the prime factorization of 1513
1513 = 17 x 89
Step 2: Find the prime factorization of 1520
1520 = 2 x 2 x 2 x 2 x 5 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2299760 = 2 x 2 x 2 x 2 x 5 x 17 x 19 x 89
Step 4: Therefore, the least common multiple of 1513 and 1520 is 2299760.