Least Common Multiple (LCM) of 83 and 68
The least common multiple (LCM) of 83 and 68 is 5644.
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 68?
First, calculate the GCD of 83 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 68 = 1 remainder 15 |
| 2 | 68 ÷ 15 = 4 remainder 8 |
| 3 | 15 ÷ 8 = 1 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 15 | 285 |
| 67 and 146 | 9782 |
| 116 and 28 | 812 |
| 193 and 140 | 27020 |
| 163 and 20 | 3260 |