Least Common Multiple (LCM) of 167 and 198
The least common multiple (LCM) of 167 and 198 is 33066.
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 167 and 198?
First, calculate the GCD of 167 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 198 = 0 remainder 167 |
| 2 | 198 ÷ 167 = 1 remainder 31 |
| 3 | 167 ÷ 31 = 5 remainder 12 |
| 4 | 31 ÷ 12 = 2 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 172 | 4472 |
| 169 and 107 | 18083 |
| 87 and 124 | 10788 |
| 182 and 14 | 182 |
| 31 and 149 | 4619 |