Least Common Multiple (LCM) of 189 and 167
The least common multiple (LCM) of 189 and 167 is 31563.
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 167?
First, calculate the GCD of 189 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 167 = 1 remainder 22 |
| 2 | 167 ÷ 22 = 7 remainder 13 |
| 3 | 22 ÷ 13 = 1 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 92 | 3772 |
| 76 and 149 | 11324 |
| 181 and 195 | 35295 |
| 80 and 11 | 880 |
| 116 and 85 | 9860 |