Least Common Multiple (LCM) of 166 and 189
The least common multiple (LCM) of 166 and 189 is 31374.
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 166 and 189?
First, calculate the GCD of 166 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 166 ÷ 189 = 0 remainder 166 |
| 2 | 189 ÷ 166 = 1 remainder 23 |
| 3 | 166 ÷ 23 = 7 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 142 | 10508 |
| 138 and 84 | 1932 |
| 177 and 98 | 17346 |
| 189 and 187 | 35343 |
| 54 and 185 | 9990 |