Least Common Multiple (LCM) of 165 and 180
The least common multiple (LCM) of 165 and 180 is 1980.
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 180?
First, calculate the GCD of 165 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 180 = 0 remainder 165 |
| 2 | 180 ÷ 165 = 1 remainder 15 |
| 3 | 165 ÷ 15 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 58 | 2494 |
| 106 and 192 | 10176 |
| 56 and 31 | 1736 |
| 137 and 32 | 4384 |
| 74 and 13 | 962 |