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 |
|---|---|
| 180 and 121 | 21780 |
| 122 and 132 | 8052 |
| 145 and 162 | 23490 |
| 128 and 97 | 12416 |
| 10 and 21 | 210 |