Least Common Multiple (LCM) of 198 and 101
The least common multiple (LCM) of 198 and 101 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 198 and 101?
First, calculate the GCD of 198 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 101 = 1 remainder 97 |
| 2 | 101 ÷ 97 = 1 remainder 4 |
| 3 | 97 ÷ 4 = 24 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 181 | 19548 |
| 180 and 43 | 7740 |
| 31 and 98 | 3038 |
| 56 and 108 | 1512 |
| 115 and 74 | 8510 |