Least Common Multiple (LCM) of 78 and 102
The least common multiple (LCM) of 78 and 102 is 1326.
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 102?
First, calculate the GCD of 78 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 102 = 0 remainder 78 |
| 2 | 102 ÷ 78 = 1 remainder 24 |
| 3 | 78 ÷ 24 = 3 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 144 | 1008 |
| 194 and 129 | 25026 |
| 184 and 38 | 3496 |
| 164 and 169 | 27716 |
| 123 and 55 | 6765 |