Least Common Multiple (LCM) of 99 and 191
The least common multiple (LCM) of 99 and 191 is 18909.
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 191?
First, calculate the GCD of 99 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 191 = 0 remainder 99 |
| 2 | 191 ÷ 99 = 1 remainder 92 |
| 3 | 99 ÷ 92 = 1 remainder 7 |
| 4 | 92 ÷ 7 = 13 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 57 | 9291 |
| 16 and 192 | 192 |
| 135 and 181 | 24435 |
| 184 and 23 | 184 |
| 105 and 131 | 13755 |