Least Common Multiple (LCM) of 75 and 128
The least common multiple (LCM) of 75 and 128 is 9600.
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 75 and 128?
First, calculate the GCD of 75 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 128 = 0 remainder 75 |
| 2 | 128 ÷ 75 = 1 remainder 53 |
| 3 | 75 ÷ 53 = 1 remainder 22 |
| 4 | 53 ÷ 22 = 2 remainder 9 |
| 5 | 22 ÷ 9 = 2 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 160 | 16160 |
| 37 and 45 | 1665 |
| 76 and 153 | 11628 |
| 108 and 140 | 3780 |
| 152 and 184 | 3496 |