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 |
|---|---|
| 179 and 175 | 31325 |
| 95 and 53 | 5035 |
| 93 and 102 | 3162 |
| 10 and 123 | 1230 |
| 163 and 120 | 19560 |