Least Common Multiple (LCM) of 199 and 101
The least common multiple (LCM) of 199 and 101 is 20099.
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 199 and 101?
First, calculate the GCD of 199 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 101 = 1 remainder 98 |
| 2 | 101 ÷ 98 = 1 remainder 3 |
| 3 | 98 ÷ 3 = 32 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 108 | 10476 |
| 162 and 28 | 2268 |
| 51 and 187 | 561 |
| 72 and 108 | 216 |
| 189 and 57 | 3591 |