Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 15178 and 15180 the smallest integer that is 115201020 that is divisible by both numbers.
Least Common Multiple (LCM) of 15178 and 15180 is 115201020.
LCM(15178,15180) = 115201020
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 15178 and 15180. First we will calculate the prime factors of 15178 and 15180.
Prime Factorization of 15178
2 | 15178 |
7589 | 7589 |
1 |
Prime factors of 15178 are 2,7589. Prime factorization of 15178 in exponential form is:
15178 = 21×75891
Prime Factorization of 15180
2 | 15180 |
2 | 7590 |
3 | 3795 |
5 | 1265 |
11 | 253 |
23 | 23 |
1 |
Prime factors of 15180 are 2, 3, 5, 11,23. Prime factorization of 15180 in exponential form is:
15180 = 22×31×51×111×231
Now multiplying the highest exponent prime factors to calculate the LCM of 15178 and 15180.
LCM(15178,15180) = 22×31×51×111×231×75891
LCM(15178,15180) = 115201020
Factors of 15178
List of positive integer factors of 15178 that divides 15178 without a remainder.
1, 2, 7589, 15178
Factors of 15180
List of positive integer factors of 15180 that divides 15180 without a remainder.
1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 23, 30, 33, 44, 46, 55, 60, 66, 69, 92, 110, 115, 132, 138, 165, 220, 230, 253, 276, 330, 345, 460, 506, 660, 690, 759, 1012, 1265, 1380, 1518, 2530, 3036, 3795, 5060, 7590, 15180
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15178 and 15180, than apply into the LCM equation.
GCF(15178,15180) = 2
LCM(15178,15180) = ( 15178 × 15180) / 2
LCM(15178,15180) = 230402040 / 2
LCM(15178,15180) = 115201020
(i) The LCM of 15180 and 15178 is associative
LCM of 15178 and 15180 = LCM of 15180 and 15178
1. What is the LCM of 15178 and 15180?
Answer: LCM of 15178 and 15180 is 115201020.
2. What are the Factors of 15178?
Answer: Factors of 15178 are 1, 2, 7589, 15178. There are 4 integers that are factors of 15178. The greatest factor of 15178 is 15178.
3. What are the Factors of 15180?
Answer: Factors of 15180 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 23, 30, 33, 44, 46, 55, 60, 66, 69, 92, 110, 115, 132, 138, 165, 220, 230, 253, 276, 330, 345, 460, 506, 660, 690, 759, 1012, 1265, 1380, 1518, 2530, 3036, 3795, 5060, 7590, 15180. There are 48 integers that are factors of 15180. The greatest factor of 15180 is 15180.
4. How to Find the LCM of 15178 and 15180?
Answer:
Least Common Multiple of 15178 and 15180 = 115201020
Step 1: Find the prime factorization of 15178
15178 = 2 x 7589
Step 2: Find the prime factorization of 15180
15180 = 2 x 2 x 3 x 5 x 11 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 115201020 = 2 x 2 x 3 x 5 x 11 x 23 x 7589
Step 4: Therefore, the least common multiple of 15178 and 15180 is 115201020.