Least Common Multiple (LCM) of 67 and 166
The least common multiple (LCM) of 67 and 166 is 11122.
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 67 and 166?
First, calculate the GCD of 67 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 166 = 0 remainder 67 |
| 2 | 166 ÷ 67 = 2 remainder 32 |
| 3 | 67 ÷ 32 = 2 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 117 | 1287 |
| 50 and 59 | 2950 |
| 161 and 75 | 12075 |
| 161 and 71 | 11431 |
| 75 and 27 | 675 |