Least Common Multiple (LCM) of 171 and 60
The least common multiple (LCM) of 171 and 60 is 3420.
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 60?
First, calculate the GCD of 171 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 60 = 2 remainder 51 |
| 2 | 60 ÷ 51 = 1 remainder 9 |
| 3 | 51 ÷ 9 = 5 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 187 | 30668 |
| 170 and 188 | 15980 |
| 34 and 45 | 1530 |
| 162 and 73 | 11826 |
| 120 and 13 | 1560 |