Least Common Multiple (LCM) of 128 and 113
The least common multiple (LCM) of 128 and 113 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 128 and 113?
First, calculate the GCD of 128 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 113 = 1 remainder 15 |
| 2 | 113 ÷ 15 = 7 remainder 8 |
| 3 | 15 ÷ 8 = 1 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 161 | 966 |
| 13 and 183 | 2379 |
| 197 and 189 | 37233 |
| 125 and 100 | 500 |
| 109 and 25 | 2725 |