Least Common Multiple (LCM) of 199 and 91
The least common multiple (LCM) of 199 and 91 is 18109.
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 91?
First, calculate the GCD of 199 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 91 = 2 remainder 17 |
| 2 | 91 ÷ 17 = 5 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 71 | 12354 |
| 124 and 13 | 1612 |
| 112 and 84 | 336 |
| 103 and 94 | 9682 |
| 153 and 46 | 7038 |