Least Common Multiple (LCM) of 193 and 99
The least common multiple (LCM) of 193 and 99 is 19107.
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 193 and 99?
First, calculate the GCD of 193 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 99 = 1 remainder 94 |
| 2 | 99 ÷ 94 = 1 remainder 5 |
| 3 | 94 ÷ 5 = 18 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 37 | 6031 |
| 57 and 187 | 10659 |
| 172 and 196 | 8428 |
| 14 and 14 | 14 |
| 37 and 96 | 3552 |