Least Common Multiple (LCM) of 165 and 65
The least common multiple (LCM) of 165 and 65 is 2145.
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 65?
First, calculate the GCD of 165 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 65 = 2 remainder 35 |
| 2 | 65 ÷ 35 = 1 remainder 30 |
| 3 | 35 ÷ 30 = 1 remainder 5 |
| 4 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 128 | 128 |
| 112 and 119 | 1904 |
| 30 and 54 | 270 |
| 101 and 116 | 11716 |
| 153 and 169 | 25857 |