Least Common Multiple (LCM) of 83 and 128
The least common multiple (LCM) of 83 and 128 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 83 and 128?
First, calculate the GCD of 83 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 128 = 0 remainder 83 |
| 2 | 128 ÷ 83 = 1 remainder 45 |
| 3 | 83 ÷ 45 = 1 remainder 38 |
| 4 | 45 ÷ 38 = 1 remainder 7 |
| 5 | 38 ÷ 7 = 5 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 10 | 1690 |
| 121 and 161 | 19481 |
| 127 and 77 | 9779 |
| 119 and 190 | 22610 |
| 117 and 122 | 14274 |