Least Common Multiple (LCM) of 109 and 128
The least common multiple (LCM) of 109 and 128 is 13952.
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 109 and 128?
First, calculate the GCD of 109 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 128 = 0 remainder 109 |
| 2 | 128 ÷ 109 = 1 remainder 19 |
| 3 | 109 ÷ 19 = 5 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 139 | 15012 |
| 200 and 119 | 23800 |
| 48 and 162 | 1296 |
| 162 and 176 | 14256 |
| 70 and 17 | 1190 |