Least Common Multiple (LCM) of 161 and 83
The least common multiple (LCM) of 161 and 83 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 161 and 83?
First, calculate the GCD of 161 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 161 ÷ 83 = 1 remainder 78 |
| 2 | 83 ÷ 78 = 1 remainder 5 |
| 3 | 78 ÷ 5 = 15 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 145 | 6815 |
| 194 and 112 | 10864 |
| 132 and 88 | 264 |
| 137 and 175 | 23975 |
| 144 and 182 | 13104 |