Least Common Multiple (LCM) of 78 and 106
The least common multiple (LCM) of 78 and 106 is 4134.
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 106?
First, calculate the GCD of 78 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 106 = 0 remainder 78 |
| 2 | 106 ÷ 78 = 1 remainder 28 |
| 3 | 78 ÷ 28 = 2 remainder 22 |
| 4 | 28 ÷ 22 = 1 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 21 | 2121 |
| 173 and 57 | 9861 |
| 10 and 130 | 130 |
| 115 and 198 | 22770 |
| 48 and 83 | 3984 |