Least Common Multiple (LCM) of 195 and 71
The least common multiple (LCM) of 195 and 71 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 195 and 71?
First, calculate the GCD of 195 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 71 = 2 remainder 53 |
| 2 | 71 ÷ 53 = 1 remainder 18 |
| 3 | 53 ÷ 18 = 2 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 70 | 2520 |
| 38 and 55 | 2090 |
| 107 and 169 | 18083 |
| 121 and 156 | 18876 |
| 182 and 73 | 13286 |