Least Common Multiple (LCM) of 171 and 103
The least common multiple (LCM) of 171 and 103 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 171 and 103?
First, calculate the GCD of 171 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 103 = 1 remainder 68 |
| 2 | 103 ÷ 68 = 1 remainder 35 |
| 3 | 68 ÷ 35 = 1 remainder 33 |
| 4 | 35 ÷ 33 = 1 remainder 2 |
| 5 | 33 ÷ 2 = 16 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 178 | 34710 |
| 45 and 118 | 5310 |
| 91 and 129 | 11739 |
| 176 and 87 | 15312 |
| 87 and 162 | 4698 |