Least Common Multiple (LCM) of 83 and 32
The least common multiple (LCM) of 83 and 32 is 2656.
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 83 and 32?
First, calculate the GCD of 83 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 32 = 2 remainder 19 |
| 2 | 32 ÷ 19 = 1 remainder 13 |
| 3 | 19 ÷ 13 = 1 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 85 | 6120 |
| 140 and 198 | 13860 |
| 32 and 50 | 800 |
| 190 and 165 | 6270 |
| 159 and 49 | 7791 |