Least Common Multiple (LCM) of 114 and 171
The least common multiple (LCM) of 114 and 171 is 342.
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 114 and 171?
First, calculate the GCD of 114 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 171 = 0 remainder 114 |
| 2 | 171 ÷ 114 = 1 remainder 57 |
| 3 | 114 ÷ 57 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 115 | 1840 |
| 116 and 73 | 8468 |
| 162 and 159 | 8586 |
| 20 and 75 | 300 |
| 82 and 60 | 2460 |