Least Common Multiple (LCM) of 71 and 196
The least common multiple (LCM) of 71 and 196 is 13916.
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 196?
First, calculate the GCD of 71 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 196 = 0 remainder 71 |
| 2 | 196 ÷ 71 = 2 remainder 54 |
| 3 | 71 ÷ 54 = 1 remainder 17 |
| 4 | 54 ÷ 17 = 3 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 199 | 31641 |
| 103 and 136 | 14008 |
| 22 and 154 | 154 |
| 155 and 24 | 3720 |
| 194 and 155 | 30070 |