Least Common Multiple (LCM) of 11 and 106
The least common multiple (LCM) of 11 and 106 is 1166.
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 11 and 106?
First, calculate the GCD of 11 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 106 = 0 remainder 11 |
| 2 | 106 ÷ 11 = 9 remainder 7 |
| 3 | 11 ÷ 7 = 1 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 197 | 27580 |
| 66 and 88 | 264 |
| 73 and 99 | 7227 |
| 151 and 80 | 12080 |
| 50 and 144 | 3600 |