Least Common Multiple (LCM) of 123 and 182
The least common multiple (LCM) of 123 and 182 is 22386.
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 123 and 182?
First, calculate the GCD of 123 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 182 = 0 remainder 123 |
| 2 | 182 ÷ 123 = 1 remainder 59 |
| 3 | 123 ÷ 59 = 2 remainder 5 |
| 4 | 59 ÷ 5 = 11 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 78 | 1482 |
| 169 and 82 | 13858 |
| 157 and 38 | 5966 |
| 165 and 99 | 495 |
| 116 and 47 | 5452 |