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 |
|---|---|
| 116 and 118 | 6844 |
| 104 and 14 | 728 |
| 48 and 196 | 2352 |
| 114 and 71 | 8094 |
| 128 and 80 | 640 |