Least Common Multiple (LCM) of 199 and 172
The least common multiple (LCM) of 199 and 172 is 34228.
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 172?
First, calculate the GCD of 199 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 172 = 1 remainder 27 |
| 2 | 172 ÷ 27 = 6 remainder 10 |
| 3 | 27 ÷ 10 = 2 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 91 | 16107 |
| 126 and 178 | 11214 |
| 125 and 33 | 4125 |
| 58 and 184 | 5336 |
| 138 and 99 | 4554 |