Least Common Multiple (LCM) of 171 and 101
The least common multiple (LCM) of 171 and 101 is 17271.
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 101?
First, calculate the GCD of 171 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 101 = 1 remainder 70 |
| 2 | 101 ÷ 70 = 1 remainder 31 |
| 3 | 70 ÷ 31 = 2 remainder 8 |
| 4 | 31 ÷ 8 = 3 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 20 | 980 |
| 99 and 117 | 1287 |
| 200 and 170 | 3400 |
| 140 and 118 | 8260 |
| 173 and 148 | 25604 |