Least Common Multiple (LCM) of 171 and 108
The least common multiple (LCM) of 171 and 108 is 2052.
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 108?
First, calculate the GCD of 171 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 108 = 1 remainder 63 |
| 2 | 108 ÷ 63 = 1 remainder 45 |
| 3 | 63 ÷ 45 = 1 remainder 18 |
| 4 | 45 ÷ 18 = 2 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 31 | 4526 |
| 125 and 28 | 3500 |
| 132 and 200 | 6600 |
| 138 and 118 | 8142 |
| 111 and 106 | 11766 |