Least Common Multiple (LCM) of 106 and 66
The least common multiple (LCM) of 106 and 66 is 3498.
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 66?
First, calculate the GCD of 106 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 66 = 1 remainder 40 |
| 2 | 66 ÷ 40 = 1 remainder 26 |
| 3 | 40 ÷ 26 = 1 remainder 14 |
| 4 | 26 ÷ 14 = 1 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 100 | 900 |
| 142 and 174 | 12354 |
| 71 and 194 | 13774 |
| 122 and 47 | 5734 |
| 190 and 161 | 30590 |