Least Common Multiple (LCM) of 198 and 178
The least common multiple (LCM) of 198 and 178 is 17622.
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 198 and 178?
First, calculate the GCD of 198 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 178 = 1 remainder 20 |
| 2 | 178 ÷ 20 = 8 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 167 | 8684 |
| 129 and 75 | 3225 |
| 175 and 64 | 11200 |
| 18 and 162 | 162 |
| 60 and 31 | 1860 |