Least Common Multiple (LCM) of 78 and 112
The least common multiple (LCM) of 78 and 112 is 4368.
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 78 and 112?
First, calculate the GCD of 78 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 112 = 0 remainder 78 |
| 2 | 112 ÷ 78 = 1 remainder 34 |
| 3 | 78 ÷ 34 = 2 remainder 10 |
| 4 | 34 ÷ 10 = 3 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 87 | 4263 |
| 106 and 185 | 19610 |
| 199 and 48 | 9552 |
| 187 and 42 | 7854 |
| 116 and 25 | 2900 |