Least Common Multiple (LCM) of 71 and 41
The least common multiple (LCM) of 71 and 41 is 2911.
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 41?
First, calculate the GCD of 71 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 41 = 1 remainder 30 |
| 2 | 41 ÷ 30 = 1 remainder 11 |
| 3 | 30 ÷ 11 = 2 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 80 | 9360 |
| 25 and 127 | 3175 |
| 194 and 32 | 3104 |
| 162 and 119 | 19278 |
| 88 and 69 | 6072 |