Least Common Multiple (LCM) of 168 and 34
The least common multiple (LCM) of 168 and 34 is 2856.
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 168 and 34?
First, calculate the GCD of 168 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 34 = 4 remainder 32 |
| 2 | 34 ÷ 32 = 1 remainder 2 |
| 3 | 32 ÷ 2 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 25 | 4200 |
| 34 and 114 | 1938 |
| 189 and 177 | 11151 |
| 163 and 35 | 5705 |
| 14 and 82 | 574 |