Least Common Multiple (LCM) of 83 and 162
The least common multiple (LCM) of 83 and 162 is 13446.
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 162?
First, calculate the GCD of 83 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 162 = 0 remainder 83 |
| 2 | 162 ÷ 83 = 1 remainder 79 |
| 3 | 83 ÷ 79 = 1 remainder 4 |
| 4 | 79 ÷ 4 = 19 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 43 | 2967 |
| 173 and 197 | 34081 |
| 113 and 183 | 20679 |
| 40 and 158 | 3160 |
| 127 and 129 | 16383 |