Least Common Multiple (LCM) of 171 and 74
The least common multiple (LCM) of 171 and 74 is 12654.
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 74?
First, calculate the GCD of 171 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 74 = 2 remainder 23 |
| 2 | 74 ÷ 23 = 3 remainder 5 |
| 3 | 23 ÷ 5 = 4 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 67 | 10318 |
| 82 and 160 | 6560 |
| 163 and 193 | 31459 |
| 114 and 20 | 1140 |
| 71 and 196 | 13916 |