Least Common Multiple (LCM) of 171 and 68
The least common multiple (LCM) of 171 and 68 is 11628.
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 68?
First, calculate the GCD of 171 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 68 = 2 remainder 35 |
| 2 | 68 ÷ 35 = 1 remainder 33 |
| 3 | 35 ÷ 33 = 1 remainder 2 |
| 4 | 33 ÷ 2 = 16 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 109 | 21146 |
| 103 and 108 | 11124 |
| 53 and 52 | 2756 |
| 150 and 91 | 13650 |
| 125 and 78 | 9750 |