Least Common Multiple (LCM) of 171 and 100
The least common multiple (LCM) of 171 and 100 is 17100.
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 100?
First, calculate the GCD of 171 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 100 = 1 remainder 71 |
| 2 | 100 ÷ 71 = 1 remainder 29 |
| 3 | 71 ÷ 29 = 2 remainder 13 |
| 4 | 29 ÷ 13 = 2 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 37 | 3737 |
| 58 and 177 | 10266 |
| 142 and 199 | 28258 |
| 83 and 85 | 7055 |
| 120 and 170 | 2040 |