Least Common Multiple (LCM) of 134 and 117
The least common multiple (LCM) of 134 and 117 is 15678.
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 134 and 117?
First, calculate the GCD of 134 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 117 = 1 remainder 17 |
| 2 | 117 ÷ 17 = 6 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 137 | 16029 |
| 117 and 173 | 20241 |
| 81 and 142 | 11502 |
| 177 and 104 | 18408 |
| 12 and 108 | 108 |