Least Common Multiple of 123 and 129
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 123 and 129 the smallest integer that is 5289 that is divisible by both numbers.
Least Common Multiple (LCM) of 123 and 129 is 5289.
LCM(123,129) = 5289
LCM of 123 and 129
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 123 and 129 by Prime method
- Least Common Multiple of 123 and 129 with GCF Formula
LCM of 123 and 129 is 5289
Least common multiple can be found by multiplying the highest exponent prime factors of 123 and 129. First we will calculate the prime factors of 123 and 129.
Prime Factorization of 123
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 123 are 3,41. Prime factorization of 123 in exponential form is:
123 = 31×411
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
Now multiplying the highest exponent prime factors to calculate the LCM of 123 and 129.
LCM(123,129) = 31×411×431
LCM(123,129) = 5289
Factors of 123
List of positive integer factors of 123 that divides 123 without a remainder.
1, 3, 41, 123
Factors of 129
List of positive integer factors of 129 that divides 129 without a remainder.
1, 3, 43, 129
Least Common Multiple of 123 and 129 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 123 and 129, than apply into the LCM equation.
GCF(123,129) = 3
LCM(123,129) = ( 123 × 129) / 3
LCM(123,129) = 15867 / 3
LCM(123,129) = 5289
Properties of LCM 123 and 129
(i) The LCM of 129 and 123 is associative
LCM of 123 and 129 = LCM of 129 and 123
Related Least Common Multiples of 123
Related Least Common Multiples of 129
Frequently Asked Questions on LCM of 123 and 129
1. What is the LCM of 123 and 129?
Answer: LCM of 123 and 129 is 5289.
2. What are the Factors of 123?
Answer: Factors of 123 are 1, 3, 41, 123. There are 4 integers that are factors of 123. The greatest factor of 123 is 123.
3. 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.
4. How to Find the LCM of 123 and 129?
Answer:
Least Common Multiple of 123 and 129 = 5289
Step 1: Find the prime factorization of 123
123 = 3 x 41
Step 2: Find the prime factorization of 129
129 = 3 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5289 = 3 x 41 x 43
Step 4: Therefore, the least common multiple of 123 and 129 is 5289.
