Least Common Multiple (LCM) of 83 and 96
The least common multiple (LCM) of 83 and 96 is 7968.
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 96?
First, calculate the GCD of 83 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 96 = 0 remainder 83 |
| 2 | 96 ÷ 83 = 1 remainder 13 |
| 3 | 83 ÷ 13 = 6 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 42 | 6510 |
| 125 and 110 | 2750 |
| 112 and 46 | 2576 |
| 82 and 16 | 656 |
| 78 and 157 | 12246 |