Least Common Multiple (LCM) of 71 and 83
The least common multiple (LCM) of 71 and 83 is 5893.
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 83?
First, calculate the GCD of 71 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 83 = 0 remainder 71 |
| 2 | 83 ÷ 71 = 1 remainder 12 |
| 3 | 71 ÷ 12 = 5 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 85 | 9435 |
| 38 and 167 | 6346 |
| 123 and 137 | 16851 |
| 112 and 46 | 2576 |
| 132 and 130 | 8580 |