Least Common Multiple (LCM) of 109 and 78
The least common multiple (LCM) of 109 and 78 is 8502.
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 109 and 78?
First, calculate the GCD of 109 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 78 = 1 remainder 31 |
| 2 | 78 ÷ 31 = 2 remainder 16 |
| 3 | 31 ÷ 16 = 1 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 54 | 270 |
| 96 and 133 | 12768 |
| 11 and 107 | 1177 |
| 46 and 191 | 8786 |
| 140 and 128 | 4480 |