Least Common Multiple (LCM) of 83 and 159
The least common multiple (LCM) of 83 and 159 is 13197.
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 159?
First, calculate the GCD of 83 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 159 = 0 remainder 83 |
| 2 | 159 ÷ 83 = 1 remainder 76 |
| 3 | 83 ÷ 76 = 1 remainder 7 |
| 4 | 76 ÷ 7 = 10 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 50 | 4300 |
| 87 and 180 | 5220 |
| 105 and 65 | 1365 |
| 123 and 177 | 7257 |
| 96 and 71 | 6816 |