Least Common Multiple (LCM) of 79 and 128
The least common multiple (LCM) of 79 and 128 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 79 and 128?
First, calculate the GCD of 79 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 79 ÷ 128 = 0 remainder 79 |
| 2 | 128 ÷ 79 = 1 remainder 49 |
| 3 | 79 ÷ 49 = 1 remainder 30 |
| 4 | 49 ÷ 30 = 1 remainder 19 |
| 5 | 30 ÷ 19 = 1 remainder 11 |
| 6 | 19 ÷ 11 = 1 remainder 8 |
| 7 | 11 ÷ 8 = 1 remainder 3 |
| 8 | 8 ÷ 3 = 2 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 157 | 30144 |
| 40 and 138 | 2760 |
| 191 and 44 | 8404 |
| 29 and 169 | 4901 |
| 18 and 194 | 1746 |