Least Common Multiple (LCM) of 68 and 41
The least common multiple (LCM) of 68 and 41 is 2788.
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 41?
First, calculate the GCD of 68 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 41 = 1 remainder 27 |
| 2 | 41 ÷ 27 = 1 remainder 14 |
| 3 | 27 ÷ 14 = 1 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 10 | 730 |
| 166 and 102 | 8466 |
| 106 and 60 | 3180 |
| 186 and 136 | 12648 |
| 144 and 129 | 6192 |