Least Common Multiple (LCM) of 123 and 165
The least common multiple (LCM) of 123 and 165 is 6765.
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 165?
First, calculate the GCD of 123 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 165 = 0 remainder 123 |
| 2 | 165 ÷ 123 = 1 remainder 42 |
| 3 | 123 ÷ 42 = 2 remainder 39 |
| 4 | 42 ÷ 39 = 1 remainder 3 |
| 5 | 39 ÷ 3 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 78 | 234 |
| 168 and 178 | 14952 |
| 117 and 171 | 2223 |
| 34 and 158 | 2686 |
| 170 and 36 | 3060 |