Least Common Multiple (LCM) of 128 and 83
The least common multiple (LCM) of 128 and 83 is 10624.
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 83?
First, calculate the GCD of 128 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 83 = 1 remainder 45 |
| 2 | 83 ÷ 45 = 1 remainder 38 |
| 3 | 45 ÷ 38 = 1 remainder 7 |
| 4 | 38 ÷ 7 = 5 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 42 | 294 |
| 31 and 40 | 1240 |
| 163 and 133 | 21679 |
| 35 and 47 | 1645 |
| 20 and 71 | 1420 |