Least Common Multiple (LCM) of 106 and 68
The least common multiple (LCM) of 106 and 68 is 3604.
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 106 and 68?
First, calculate the GCD of 106 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 68 = 1 remainder 38 |
| 2 | 68 ÷ 38 = 1 remainder 30 |
| 3 | 38 ÷ 30 = 1 remainder 8 |
| 4 | 30 ÷ 8 = 3 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 14 | 154 |
| 10 and 151 | 1510 |
| 132 and 149 | 19668 |
| 102 and 152 | 7752 |
| 10 and 177 | 1770 |