Least Common Multiple (LCM) of 103 and 165
The least common multiple (LCM) of 103 and 165 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 103 and 165?
First, calculate the GCD of 103 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 165 = 0 remainder 103 |
| 2 | 165 ÷ 103 = 1 remainder 62 |
| 3 | 103 ÷ 62 = 1 remainder 41 |
| 4 | 62 ÷ 41 = 1 remainder 21 |
| 5 | 41 ÷ 21 = 1 remainder 20 |
| 6 | 21 ÷ 20 = 1 remainder 1 |
| 7 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 199 | 23482 |
| 147 and 133 | 2793 |
| 85 and 66 | 5610 |
| 66 and 182 | 6006 |
| 116 and 34 | 1972 |