Least Common Multiple (LCM) of 112 and 138
The least common multiple (LCM) of 112 and 138 is 7728.
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 112 and 138?
First, calculate the GCD of 112 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 138 = 0 remainder 112 |
| 2 | 138 ÷ 112 = 1 remainder 26 |
| 3 | 112 ÷ 26 = 4 remainder 8 |
| 4 | 26 ÷ 8 = 3 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 157 | 10205 |
| 86 and 125 | 10750 |
| 138 and 162 | 3726 |
| 133 and 190 | 1330 |
| 150 and 47 | 7050 |