Least Common Multiple (LCM) of 20 and 165
The least common multiple (LCM) of 20 and 165 is 660.
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 20 and 165?
First, calculate the GCD of 20 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 165 = 0 remainder 20 |
| 2 | 165 ÷ 20 = 8 remainder 5 |
| 3 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 54 | 10422 |
| 141 and 61 | 8601 |
| 40 and 78 | 1560 |
| 125 and 81 | 10125 |
| 74 and 105 | 7770 |