Least Common Multiple (LCM) of 171 and 196
The least common multiple (LCM) of 171 and 196 is 33516.
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 196?
First, calculate the GCD of 171 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 196 = 0 remainder 171 |
| 2 | 196 ÷ 171 = 1 remainder 25 |
| 3 | 171 ÷ 25 = 6 remainder 21 |
| 4 | 25 ÷ 21 = 1 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 83 | 5561 |
| 162 and 178 | 14418 |
| 145 and 22 | 3190 |
| 133 and 89 | 11837 |
| 47 and 78 | 3666 |