Least Common Multiple (LCM) of 71 and 195
The least common multiple (LCM) of 71 and 195 is 13845.
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 195?
First, calculate the GCD of 71 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 195 = 0 remainder 71 |
| 2 | 195 ÷ 71 = 2 remainder 53 |
| 3 | 71 ÷ 53 = 1 remainder 18 |
| 4 | 53 ÷ 18 = 2 remainder 17 |
| 5 | 18 ÷ 17 = 1 remainder 1 |
| 6 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 152 | 15048 |
| 21 and 150 | 1050 |
| 49 and 101 | 4949 |
| 40 and 24 | 120 |
| 90 and 100 | 900 |