Least Common Multiple (LCM) of 78 and 108
The least common multiple (LCM) of 78 and 108 is 1404.
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 108?
First, calculate the GCD of 78 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 108 = 0 remainder 78 |
| 2 | 108 ÷ 78 = 1 remainder 30 |
| 3 | 78 ÷ 30 = 2 remainder 18 |
| 4 | 30 ÷ 18 = 1 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 174 | 1566 |
| 152 and 40 | 760 |
| 165 and 132 | 660 |
| 145 and 170 | 4930 |
| 108 and 89 | 9612 |