Least Common Multiple (LCM) of 101 and 198
The least common multiple (LCM) of 101 and 198 is 19998.
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 101 and 198?
First, calculate the GCD of 101 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 198 = 0 remainder 101 |
| 2 | 198 ÷ 101 = 1 remainder 97 |
| 3 | 101 ÷ 97 = 1 remainder 4 |
| 4 | 97 ÷ 4 = 24 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 100 | 4300 |
| 106 and 61 | 6466 |
| 73 and 191 | 13943 |
| 195 and 59 | 11505 |
| 35 and 17 | 595 |