Least Common Multiple (LCM) of 107 and 78
The least common multiple (LCM) of 107 and 78 is 8346.
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 107 and 78?
First, calculate the GCD of 107 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 78 = 1 remainder 29 |
| 2 | 78 ÷ 29 = 2 remainder 20 |
| 3 | 29 ÷ 20 = 1 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 23 | 3818 |
| 75 and 200 | 600 |
| 120 and 123 | 4920 |
| 48 and 176 | 528 |
| 189 and 125 | 23625 |