Least Common Multiple (LCM) of 171 and 194
The least common multiple (LCM) of 171 and 194 is 33174.
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 194?
First, calculate the GCD of 171 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 194 = 0 remainder 171 |
| 2 | 194 ÷ 171 = 1 remainder 23 |
| 3 | 171 ÷ 23 = 7 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 110 | 3960 |
| 61 and 176 | 10736 |
| 172 and 186 | 15996 |
| 160 and 104 | 2080 |
| 62 and 78 | 2418 |