Least Common Multiple (LCM) of 138 and 113
The least common multiple (LCM) of 138 and 113 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 138 and 113?
First, calculate the GCD of 138 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 113 = 1 remainder 25 |
| 2 | 113 ÷ 25 = 4 remainder 13 |
| 3 | 25 ÷ 13 = 1 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 94 | 7426 |
| 76 and 63 | 4788 |
| 125 and 15 | 375 |
| 177 and 31 | 5487 |
| 162 and 48 | 1296 |