Least Common Multiple (LCM) of 83 and 161
The least common multiple (LCM) of 83 and 161 is 13363.
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 161?
First, calculate the GCD of 83 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 161 = 0 remainder 83 |
| 2 | 161 ÷ 83 = 1 remainder 78 |
| 3 | 83 ÷ 78 = 1 remainder 5 |
| 4 | 78 ÷ 5 = 15 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 |
|---|---|
| 13 and 98 | 1274 |
| 146 and 160 | 11680 |
| 196 and 156 | 7644 |
| 196 and 179 | 35084 |
| 178 and 133 | 23674 |