Least Common Multiple (LCM) of 65 and 165
The least common multiple (LCM) of 65 and 165 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 65 and 165?
First, calculate the GCD of 65 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 165 = 0 remainder 65 |
| 2 | 165 ÷ 65 = 2 remainder 35 |
| 3 | 65 ÷ 35 = 1 remainder 30 |
| 4 | 35 ÷ 30 = 1 remainder 5 |
| 5 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 31 | 1395 |
| 194 and 113 | 21922 |
| 17 and 103 | 1751 |
| 170 and 128 | 10880 |
| 37 and 22 | 814 |