Least Common Multiple (LCM) of 80 and 165
The least common multiple (LCM) of 80 and 165 is 2640.
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 80 and 165?
First, calculate the GCD of 80 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 165 = 0 remainder 80 |
| 2 | 165 ÷ 80 = 2 remainder 5 |
| 3 | 80 ÷ 5 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 80 | 4560 |
| 174 and 69 | 4002 |
| 12 and 112 | 336 |
| 131 and 135 | 17685 |
| 31 and 73 | 2263 |