Least Common Multiple (LCM) of 83 and 116
The least common multiple (LCM) of 83 and 116 is 9628.
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 116?
First, calculate the GCD of 83 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 116 = 0 remainder 83 |
| 2 | 116 ÷ 83 = 1 remainder 33 |
| 3 | 83 ÷ 33 = 2 remainder 17 |
| 4 | 33 ÷ 17 = 1 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 127 | 16383 |
| 192 and 144 | 576 |
| 167 and 36 | 6012 |
| 58 and 178 | 5162 |
| 107 and 16 | 1712 |