Least Common Multiple (LCM) of 97 and 171
The least common multiple (LCM) of 97 and 171 is 16587.
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 97 and 171?
First, calculate the GCD of 97 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 171 = 0 remainder 97 |
| 2 | 171 ÷ 97 = 1 remainder 74 |
| 3 | 97 ÷ 74 = 1 remainder 23 |
| 4 | 74 ÷ 23 = 3 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 110 | 1870 |
| 77 and 123 | 9471 |
| 33 and 86 | 2838 |
| 181 and 58 | 10498 |
| 73 and 149 | 10877 |