Least Common Multiple (LCM) of 67 and 171
The least common multiple (LCM) of 67 and 171 is 11457.
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 67 and 171?
First, calculate the GCD of 67 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 171 = 0 remainder 67 |
| 2 | 171 ÷ 67 = 2 remainder 37 |
| 3 | 67 ÷ 37 = 1 remainder 30 |
| 4 | 37 ÷ 30 = 1 remainder 7 |
| 5 | 30 ÷ 7 = 4 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 134 | 14874 |
| 14 and 46 | 322 |
| 13 and 85 | 1105 |
| 195 and 43 | 8385 |
| 21 and 107 | 2247 |