Least Common Multiple (LCM) of 171 and 199
The least common multiple (LCM) of 171 and 199 is 34029.
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 171 and 199?
First, calculate the GCD of 171 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 199 = 0 remainder 171 |
| 2 | 199 ÷ 171 = 1 remainder 28 |
| 3 | 171 ÷ 28 = 6 remainder 3 |
| 4 | 28 ÷ 3 = 9 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 120 | 840 |
| 122 and 116 | 7076 |
| 69 and 16 | 1104 |
| 167 and 55 | 9185 |
| 60 and 55 | 660 |