Least Common Multiple (LCM) of 103 and 171
The least common multiple (LCM) of 103 and 171 is 17613.
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 171?
First, calculate the GCD of 103 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 171 = 0 remainder 103 |
| 2 | 171 ÷ 103 = 1 remainder 68 |
| 3 | 103 ÷ 68 = 1 remainder 35 |
| 4 | 68 ÷ 35 = 1 remainder 33 |
| 5 | 35 ÷ 33 = 1 remainder 2 |
| 6 | 33 ÷ 2 = 16 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 189 | 32130 |
| 72 and 32 | 288 |
| 86 and 187 | 16082 |
| 103 and 156 | 16068 |
| 78 and 54 | 702 |