Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 171 and 177 the smallest integer that is 10089 that is divisible by both numbers.
Least Common Multiple (LCM) of 171 and 177 is 10089.
LCM(171,177) = 10089
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 171 and 177. First we will calculate the prime factors of 171 and 177.
Prime Factorization of 171
3 | 171 |
3 | 57 |
19 | 19 |
1 |
Prime factors of 171 are 3,19. Prime factorization of 171 in exponential form is:
171 = 32×191
Prime Factorization of 177
3 | 177 |
59 | 59 |
1 |
Prime factors of 177 are 3,59. Prime factorization of 177 in exponential form is:
177 = 31×591
Now multiplying the highest exponent prime factors to calculate the LCM of 171 and 177.
LCM(171,177) = 32×191×591
LCM(171,177) = 10089
Factors of 171
List of positive integer factors of 171 that divides 171 without a remainder.
1, 3, 9, 19, 57, 171
Factors of 177
List of positive integer factors of 177 that divides 177 without a remainder.
1, 3, 59, 177
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 171 and 177, than apply into the LCM equation.
GCF(171,177) = 3
LCM(171,177) = ( 171 × 177) / 3
LCM(171,177) = 30267 / 3
LCM(171,177) = 10089
(i) The LCM of 177 and 171 is associative
LCM of 171 and 177 = LCM of 177 and 171
1. What is the LCM of 171 and 177?
Answer: LCM of 171 and 177 is 10089.
2. What are the Factors of 171?
Answer: Factors of 171 are 1, 3, 9, 19, 57, 171. There are 6 integers that are factors of 171. The greatest factor of 171 is 171.
3. What are the Factors of 177?
Answer: Factors of 177 are 1, 3, 59, 177. There are 4 integers that are factors of 177. The greatest factor of 177 is 177.
4. How to Find the LCM of 171 and 177?
Answer:
Least Common Multiple of 171 and 177 = 10089
Step 1: Find the prime factorization of 171
171 = 3 x 3 x 19
Step 2: Find the prime factorization of 177
177 = 3 x 59
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 10089 = 3 x 3 x 19 x 59
Step 4: Therefore, the least common multiple of 171 and 177 is 10089.