Least Common Multiple (LCM) of 71 and 45
The least common multiple (LCM) of 71 and 45 is 3195.
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 45?
First, calculate the GCD of 71 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 45 = 1 remainder 26 |
| 2 | 45 ÷ 26 = 1 remainder 19 |
| 3 | 26 ÷ 19 = 1 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 69 | 3243 |
| 37 and 62 | 2294 |
| 186 and 165 | 10230 |
| 19 and 83 | 1577 |
| 174 and 121 | 21054 |