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 |
|---|---|
| 90 and 156 | 2340 |
| 156 and 26 | 156 |
| 117 and 42 | 1638 |
| 12 and 55 | 660 |
| 175 and 31 | 5425 |