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 |
|---|---|
| 133 and 20 | 2660 |
| 197 and 23 | 4531 |
| 189 and 104 | 19656 |
| 138 and 178 | 12282 |
| 155 and 116 | 17980 |