Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 188 and 195 the smallest integer that is 36660 that is divisible by both numbers.
Least Common Multiple (LCM) of 188 and 195 is 36660.
LCM(188,195) = 36660
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 188 and 195. First we will calculate the prime factors of 188 and 195.
Prime Factorization of 188
2 | 188 |
2 | 94 |
47 | 47 |
1 |
Prime factors of 188 are 2,47. Prime factorization of 188 in exponential form is:
188 = 22×471
Prime Factorization of 195
3 | 195 |
5 | 65 |
13 | 13 |
1 |
Prime factors of 195 are 3, 5,13. Prime factorization of 195 in exponential form is:
195 = 31×51×131
Now multiplying the highest exponent prime factors to calculate the LCM of 188 and 195.
LCM(188,195) = 22×31×51×131×471
LCM(188,195) = 36660
Factors of 188
List of positive integer factors of 188 that divides 188 without a remainder.
1, 2, 4, 47, 94, 188
Factors of 195
List of positive integer factors of 195 that divides 195 without a remainder.
1, 3, 5, 13, 15, 39, 65, 195
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 188 and 195, than apply into the LCM equation.
GCF(188,195) = 1
LCM(188,195) = ( 188 × 195) / 1
LCM(188,195) = 36660 / 1
LCM(188,195) = 36660
(i) The LCM of 195 and 188 is associative
LCM of 188 and 195 = LCM of 195 and 188
1. What is the LCM of 188 and 195?
Answer: LCM of 188 and 195 is 36660.
2. What are the Factors of 188?
Answer: Factors of 188 are 1, 2, 4, 47, 94, 188. There are 6 integers that are factors of 188. The greatest factor of 188 is 188.
3. What are the Factors of 195?
Answer: Factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195. There are 8 integers that are factors of 195. The greatest factor of 195 is 195.
4. How to Find the LCM of 188 and 195?
Answer:
Least Common Multiple of 188 and 195 = 36660
Step 1: Find the prime factorization of 188
188 = 2 x 2 x 47
Step 2: Find the prime factorization of 195
195 = 3 x 5 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 36660 = 2 x 2 x 3 x 5 x 13 x 47
Step 4: Therefore, the least common multiple of 188 and 195 is 36660.