Least Common Multiple (LCM) of 67 and 128
The least common multiple (LCM) of 67 and 128 is 8576.
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 67 and 128?
First, calculate the GCD of 67 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 128 = 0 remainder 67 |
| 2 | 128 ÷ 67 = 1 remainder 61 |
| 3 | 67 ÷ 61 = 1 remainder 6 |
| 4 | 61 ÷ 6 = 10 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 108 | 2052 |
| 114 and 142 | 8094 |
| 115 and 161 | 805 |
| 164 and 32 | 1312 |
| 95 and 95 | 95 |