Least Common Multiple (LCM) of 128 and 137
The least common multiple (LCM) of 128 and 137 is 17536.
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 137?
First, calculate the GCD of 128 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 137 = 0 remainder 128 |
| 2 | 137 ÷ 128 = 1 remainder 9 |
| 3 | 128 ÷ 9 = 14 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 10 | 1770 |
| 107 and 20 | 2140 |
| 114 and 111 | 4218 |
| 143 and 159 | 22737 |
| 180 and 80 | 720 |