Least Common Multiple (LCM) of 165 and 60
The least common multiple (LCM) of 165 and 60 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 165 and 60?
First, calculate the GCD of 165 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 60 = 2 remainder 45 |
| 2 | 60 ÷ 45 = 1 remainder 15 |
| 3 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 192 | 192 |
| 55 and 109 | 5995 |
| 153 and 85 | 765 |
| 129 and 112 | 14448 |
| 110 and 145 | 3190 |