Least Common Multiple (LCM) of 171 and 178
The least common multiple (LCM) of 171 and 178 is 30438.
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 178?
First, calculate the GCD of 171 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 178 = 0 remainder 171 |
| 2 | 178 ÷ 171 = 1 remainder 7 |
| 3 | 171 ÷ 7 = 24 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 189 | 20601 |
| 103 and 145 | 14935 |
| 21 and 20 | 420 |
| 185 and 90 | 3330 |
| 136 and 187 | 1496 |