Least Common Multiple (LCM) of 178 and 198
The least common multiple (LCM) of 178 and 198 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 178 and 198?
First, calculate the GCD of 178 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 198 = 0 remainder 178 |
| 2 | 198 ÷ 178 = 1 remainder 20 |
| 3 | 178 ÷ 20 = 8 remainder 18 |
| 4 | 20 ÷ 18 = 1 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 105 | 1050 |
| 16 and 19 | 304 |
| 73 and 111 | 8103 |
| 31 and 154 | 4774 |
| 117 and 198 | 2574 |