Least Common Multiple (LCM) of 71 and 178
The least common multiple (LCM) of 71 and 178 is 12638.
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 71 and 178?
First, calculate the GCD of 71 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 178 = 0 remainder 71 |
| 2 | 178 ÷ 71 = 2 remainder 36 |
| 3 | 71 ÷ 36 = 1 remainder 35 |
| 4 | 36 ÷ 35 = 1 remainder 1 |
| 5 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 96 | 2784 |
| 189 and 65 | 12285 |
| 43 and 162 | 6966 |
| 57 and 33 | 627 |
| 84 and 200 | 4200 |