Least Common Multiple (LCM) of 99 and 192
The least common multiple (LCM) of 99 and 192 is 6336.
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 99 and 192?
First, calculate the GCD of 99 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 192 = 0 remainder 99 |
| 2 | 192 ÷ 99 = 1 remainder 93 |
| 3 | 99 ÷ 93 = 1 remainder 6 |
| 4 | 93 ÷ 6 = 15 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 198 | 11682 |
| 48 and 167 | 8016 |
| 138 and 58 | 4002 |
| 80 and 172 | 3440 |
| 117 and 46 | 5382 |