Least Common Multiple (LCM) of 171 and 97
The least common multiple (LCM) of 171 and 97 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 171 and 97?
First, calculate the GCD of 171 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 97 = 1 remainder 74 |
| 2 | 97 ÷ 74 = 1 remainder 23 |
| 3 | 74 ÷ 23 = 3 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 177 | 25665 |
| 190 and 50 | 950 |
| 37 and 189 | 6993 |
| 149 and 13 | 1937 |
| 154 and 121 | 1694 |