Least Common Multiple (LCM) of 128 and 101
The least common multiple (LCM) of 128 and 101 is 12928.
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 101?
First, calculate the GCD of 128 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 101 = 1 remainder 27 |
| 2 | 101 ÷ 27 = 3 remainder 20 |
| 3 | 27 ÷ 20 = 1 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 138 | 3450 |
| 156 and 140 | 5460 |
| 100 and 178 | 8900 |
| 61 and 106 | 6466 |
| 31 and 195 | 6045 |