Least Common Multiple (LCM) of 99 and 194
The least common multiple (LCM) of 99 and 194 is 19206.
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 194?
First, calculate the GCD of 99 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 194 = 0 remainder 99 |
| 2 | 194 ÷ 99 = 1 remainder 95 |
| 3 | 99 ÷ 95 = 1 remainder 4 |
| 4 | 95 ÷ 4 = 23 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 119 | 14518 |
| 117 and 133 | 15561 |
| 45 and 177 | 2655 |
| 186 and 114 | 3534 |
| 10 and 85 | 170 |