Least Common Multiple (LCM) of 165 and 103
The least common multiple (LCM) of 165 and 103 is 16995.
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 103?
First, calculate the GCD of 165 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 103 = 1 remainder 62 |
| 2 | 103 ÷ 62 = 1 remainder 41 |
| 3 | 62 ÷ 41 = 1 remainder 21 |
| 4 | 41 ÷ 21 = 1 remainder 20 |
| 5 | 21 ÷ 20 = 1 remainder 1 |
| 6 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 30 | 2310 |
| 65 and 159 | 10335 |
| 183 and 84 | 5124 |
| 118 and 144 | 8496 |
| 27 and 91 | 2457 |