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 |
|---|---|
| 20 and 87 | 1740 |
| 68 and 177 | 12036 |
| 189 and 173 | 32697 |
| 48 and 186 | 1488 |
| 164 and 196 | 8036 |