Least Common Multiple (LCM) of 138 and 112
The least common multiple (LCM) of 138 and 112 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 138 and 112?
First, calculate the GCD of 138 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 112 = 1 remainder 26 |
| 2 | 112 ÷ 26 = 4 remainder 8 |
| 3 | 26 ÷ 8 = 3 remainder 2 |
| 4 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 151 | 11778 |
| 102 and 14 | 714 |
| 143 and 87 | 12441 |
| 143 and 20 | 2860 |
| 78 and 28 | 1092 |