Least Common Multiple (LCM) of 165 and 123
The least common multiple (LCM) of 165 and 123 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 165 and 123?
First, calculate the GCD of 165 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 123 = 1 remainder 42 |
| 2 | 123 ÷ 42 = 2 remainder 39 |
| 3 | 42 ÷ 39 = 1 remainder 3 |
| 4 | 39 ÷ 3 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 113 | 11300 |
| 173 and 77 | 13321 |
| 196 and 158 | 15484 |
| 162 and 37 | 5994 |
| 47 and 160 | 7520 |