Least Common Multiple (LCM) of 68 and 128
The least common multiple (LCM) of 68 and 128 is 2176.
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 128?
First, calculate the GCD of 68 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 128 = 0 remainder 68 |
| 2 | 128 ÷ 68 = 1 remainder 60 |
| 3 | 68 ÷ 60 = 1 remainder 8 |
| 4 | 60 ÷ 8 = 7 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 78 | 7332 |
| 163 and 83 | 13529 |
| 157 and 120 | 18840 |
| 197 and 133 | 26201 |
| 75 and 199 | 14925 |