Least Common Multiple (LCM) of 123 and 166
The least common multiple (LCM) of 123 and 166 is 20418.
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 166?
First, calculate the GCD of 123 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 166 = 0 remainder 123 |
| 2 | 166 ÷ 123 = 1 remainder 43 |
| 3 | 123 ÷ 43 = 2 remainder 37 |
| 4 | 43 ÷ 37 = 1 remainder 6 |
| 5 | 37 ÷ 6 = 6 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 75 | 75 |
| 37 and 149 | 5513 |
| 66 and 91 | 6006 |
| 199 and 96 | 19104 |
| 198 and 90 | 990 |