Least Common Multiple (LCM) of 119 and 128
The least common multiple (LCM) of 119 and 128 is 15232.
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 119 and 128?
First, calculate the GCD of 119 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 128 = 0 remainder 119 |
| 2 | 128 ÷ 119 = 1 remainder 9 |
| 3 | 119 ÷ 9 = 13 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 77 | 5621 |
| 122 and 121 | 14762 |
| 128 and 77 | 9856 |
| 188 and 25 | 4700 |
| 20 and 51 | 1020 |