Least Common Multiple (LCM) of 128 and 108
The least common multiple (LCM) of 128 and 108 is 3456.
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 128 and 108?
First, calculate the GCD of 128 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 108 = 1 remainder 20 |
| 2 | 108 ÷ 20 = 5 remainder 8 |
| 3 | 20 ÷ 8 = 2 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 30 | 690 |
| 19 and 104 | 1976 |
| 48 and 39 | 624 |
| 12 and 109 | 1308 |
| 63 and 42 | 126 |