Least Common Multiple (LCM) of 102 and 128
The least common multiple (LCM) of 102 and 128 is 6528.
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 102 and 128?
First, calculate the GCD of 102 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 128 = 0 remainder 102 |
| 2 | 128 ÷ 102 = 1 remainder 26 |
| 3 | 102 ÷ 26 = 3 remainder 24 |
| 4 | 26 ÷ 24 = 1 remainder 2 |
| 5 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 160 | 5280 |
| 135 and 115 | 3105 |
| 117 and 57 | 2223 |
| 105 and 24 | 840 |
| 200 and 72 | 1800 |