Least Common Multiple (LCM) of 171 and 200
The least common multiple (LCM) of 171 and 200 is 34200.
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 200?
First, calculate the GCD of 171 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 200 = 0 remainder 171 |
| 2 | 200 ÷ 171 = 1 remainder 29 |
| 3 | 171 ÷ 29 = 5 remainder 26 |
| 4 | 29 ÷ 26 = 1 remainder 3 |
| 5 | 26 ÷ 3 = 8 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 60 | 600 |
| 69 and 150 | 3450 |
| 28 and 48 | 336 |
| 194 and 57 | 11058 |
| 32 and 42 | 672 |