Least Common Multiple (LCM) of 68 and 171
The least common multiple (LCM) of 68 and 171 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 68 and 171?
First, calculate the GCD of 68 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 171 = 0 remainder 68 |
| 2 | 171 ÷ 68 = 2 remainder 35 |
| 3 | 68 ÷ 35 = 1 remainder 33 |
| 4 | 35 ÷ 33 = 1 remainder 2 |
| 5 | 33 ÷ 2 = 16 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 68 | 9724 |
| 88 and 66 | 264 |
| 62 and 124 | 124 |
| 143 and 40 | 5720 |
| 60 and 14 | 420 |