Least Common Multiple (LCM) of 128 and 79
The least common multiple (LCM) of 128 and 79 is 10112.
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 79?
First, calculate the GCD of 128 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 79 = 1 remainder 49 |
| 2 | 79 ÷ 49 = 1 remainder 30 |
| 3 | 49 ÷ 30 = 1 remainder 19 |
| 4 | 30 ÷ 19 = 1 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 184 | 18216 |
| 37 and 85 | 3145 |
| 106 and 132 | 6996 |
| 105 and 128 | 13440 |
| 193 and 110 | 21230 |