Least Common Multiple (LCM) of 104 and 68
The least common multiple (LCM) of 104 and 68 is 1768.
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 104 and 68?
First, calculate the GCD of 104 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 68 = 1 remainder 36 |
| 2 | 68 ÷ 36 = 1 remainder 32 |
| 3 | 36 ÷ 32 = 1 remainder 4 |
| 4 | 32 ÷ 4 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 71 | 1988 |
| 84 and 29 | 2436 |
| 146 and 78 | 5694 |
| 104 and 128 | 1664 |
| 199 and 198 | 39402 |