Least Common Multiple (LCM) of 106 and 116
The least common multiple (LCM) of 106 and 116 is 6148.
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 116?
First, calculate the GCD of 106 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 116 = 0 remainder 106 |
| 2 | 116 ÷ 106 = 1 remainder 10 |
| 3 | 106 ÷ 10 = 10 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 105 | 2310 |
| 127 and 42 | 5334 |
| 137 and 179 | 24523 |
| 146 and 106 | 7738 |
| 18 and 68 | 612 |