Least Common Multiple (LCM) of 114 and 78
The least common multiple (LCM) of 114 and 78 is 1482.
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 114 and 78?
First, calculate the GCD of 114 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 78 = 1 remainder 36 |
| 2 | 78 ÷ 36 = 2 remainder 6 |
| 3 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 163 | 20864 |
| 177 and 82 | 14514 |
| 102 and 32 | 1632 |
| 152 and 83 | 12616 |
| 162 and 60 | 1620 |