Least Common Multiple (LCM) of 113 and 128
The least common multiple (LCM) of 113 and 128 is 14464.
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 113 and 128?
First, calculate the GCD of 113 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 128 = 0 remainder 113 |
| 2 | 128 ÷ 113 = 1 remainder 15 |
| 3 | 113 ÷ 15 = 7 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 31 | 5828 |
| 67 and 42 | 2814 |
| 190 and 54 | 5130 |
| 197 and 44 | 8668 |
| 190 and 188 | 17860 |