Least Common Multiple (LCM) of 107 and 128
The least common multiple (LCM) of 107 and 128 is 13696.
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 107 and 128?
First, calculate the GCD of 107 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 128 = 0 remainder 107 |
| 2 | 128 ÷ 107 = 1 remainder 21 |
| 3 | 107 ÷ 21 = 5 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 79 | 6715 |
| 118 and 180 | 10620 |
| 135 and 173 | 23355 |
| 71 and 112 | 7952 |
| 191 and 150 | 28650 |