Least Common Multiple (LCM) of 171 and 59
The least common multiple (LCM) of 171 and 59 is 10089.
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 59?
First, calculate the GCD of 171 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 59 = 2 remainder 53 |
| 2 | 59 ÷ 53 = 1 remainder 6 |
| 3 | 53 ÷ 6 = 8 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 177 | 18408 |
| 69 and 63 | 1449 |
| 19 and 190 | 190 |
| 192 and 48 | 192 |
| 60 and 120 | 120 |