Least Common Multiple (LCM) of 189 and 166
The least common multiple (LCM) of 189 and 166 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 189 and 166?
First, calculate the GCD of 189 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 166 = 1 remainder 23 |
| 2 | 166 ÷ 23 = 7 remainder 5 |
| 3 | 23 ÷ 5 = 4 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 38 | 2926 |
| 39 and 111 | 1443 |
| 134 and 116 | 7772 |
| 142 and 178 | 12638 |
| 161 and 67 | 10787 |