Least Common Multiple (LCM) of 71 and 93
The least common multiple (LCM) of 71 and 93 is 6603.
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 93?
First, calculate the GCD of 71 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 93 = 0 remainder 71 |
| 2 | 93 ÷ 71 = 1 remainder 22 |
| 3 | 71 ÷ 22 = 3 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 135 | 2970 |
| 101 and 82 | 8282 |
| 188 and 15 | 2820 |
| 61 and 45 | 2745 |
| 135 and 81 | 405 |