Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 129 and 133 the smallest integer that is 17157 that is divisible by both numbers.
Least Common Multiple (LCM) of 129 and 133 is 17157.
LCM(129,133) = 17157
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 129 and 133. First we will calculate the prime factors of 129 and 133.
Prime Factorization of 129
3 | 129 |
43 | 43 |
1 |
Prime factors of 129 are 3,43. Prime factorization of 129 in exponential form is:
129 = 31×431
Prime Factorization of 133
7 | 133 |
19 | 19 |
1 |
Prime factors of 133 are 7,19. Prime factorization of 133 in exponential form is:
133 = 71×191
Now multiplying the highest exponent prime factors to calculate the LCM of 129 and 133.
LCM(129,133) = 31×71×191×431
LCM(129,133) = 17157
Factors of 129
List of positive integer factors of 129 that divides 129 without a remainder.
1, 3, 43, 129
Factors of 133
List of positive integer factors of 133 that divides 133 without a remainder.
1, 7, 19, 133
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 129 and 133, than apply into the LCM equation.
GCF(129,133) = 1
LCM(129,133) = ( 129 × 133) / 1
LCM(129,133) = 17157 / 1
LCM(129,133) = 17157
(i) The LCM of 133 and 129 is associative
LCM of 129 and 133 = LCM of 133 and 129
1. What is the LCM of 129 and 133?
Answer: LCM of 129 and 133 is 17157.
2. What are the Factors of 129?
Answer: Factors of 129 are 1, 3, 43, 129. There are 4 integers that are factors of 129. The greatest factor of 129 is 129.
3. What are the Factors of 133?
Answer: Factors of 133 are 1, 7, 19, 133. There are 4 integers that are factors of 133. The greatest factor of 133 is 133.
4. How to Find the LCM of 129 and 133?
Answer:
Least Common Multiple of 129 and 133 = 17157
Step 1: Find the prime factorization of 129
129 = 3 x 43
Step 2: Find the prime factorization of 133
133 = 7 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 = 17157 = 3 x 7 x 19 x 43
Step 4: Therefore, the least common multiple of 129 and 133 is 17157.