Least Common Multiple (LCM) of 129 and 13
The least common multiple (LCM) of 129 and 13 is 1677.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 129 and 13?
First, calculate the GCD of 129 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 13 = 9 remainder 12 |
| 2 | 13 ÷ 12 = 1 remainder 1 |
| 3 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 87 | 2262 |
| 194 and 28 | 2716 |
| 44 and 31 | 1364 |
| 106 and 166 | 8798 |
| 54 and 42 | 378 |