Least Common Multiple (LCM) of 78 and 86
The least common multiple (LCM) of 78 and 86 is 3354.
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 86?
First, calculate the GCD of 78 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 86 = 0 remainder 78 |
| 2 | 86 ÷ 78 = 1 remainder 8 |
| 3 | 78 ÷ 8 = 9 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 106 | 19186 |
| 102 and 37 | 3774 |
| 104 and 78 | 312 |
| 171 and 120 | 6840 |
| 169 and 78 | 1014 |