Least Common Multiple (LCM) of 103 and 128
The least common multiple (LCM) of 103 and 128 is 13184.
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 103 and 128?
First, calculate the GCD of 103 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 128 = 0 remainder 103 |
| 2 | 128 ÷ 103 = 1 remainder 25 |
| 3 | 103 ÷ 25 = 4 remainder 3 |
| 4 | 25 ÷ 3 = 8 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 170 | 4420 |
| 70 and 193 | 13510 |
| 44 and 139 | 6116 |
| 72 and 94 | 3384 |
| 115 and 23 | 115 |