Least Common Multiple (LCM) of 59 and 128
The least common multiple (LCM) of 59 and 128 is 7552.
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 59 and 128?
First, calculate the GCD of 59 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 128 = 0 remainder 59 |
| 2 | 128 ÷ 59 = 2 remainder 10 |
| 3 | 59 ÷ 10 = 5 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 165 | 1485 |
| 77 and 117 | 9009 |
| 176 and 192 | 2112 |
| 54 and 35 | 1890 |
| 146 and 193 | 28178 |