Least Common Multiple (LCM) of 83 and 105
The least common multiple (LCM) of 83 and 105 is 8715.
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 105?
First, calculate the GCD of 83 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 105 = 0 remainder 83 |
| 2 | 105 ÷ 83 = 1 remainder 22 |
| 3 | 83 ÷ 22 = 3 remainder 17 |
| 4 | 22 ÷ 17 = 1 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 55 | 8360 |
| 163 and 16 | 2608 |
| 77 and 142 | 10934 |
| 10 and 89 | 890 |
| 148 and 181 | 26788 |