Least Common Multiple (LCM) of 113 and 138
The least common multiple (LCM) of 113 and 138 is 15594.
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 138?
First, calculate the GCD of 113 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 138 = 0 remainder 113 |
| 2 | 138 ÷ 113 = 1 remainder 25 |
| 3 | 113 ÷ 25 = 4 remainder 13 |
| 4 | 25 ÷ 13 = 1 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 53 | 2915 |
| 23 and 38 | 874 |
| 162 and 159 | 8586 |
| 65 and 189 | 12285 |
| 86 and 57 | 4902 |