Least Common Multiple (LCM) of 106 and 111
The least common multiple (LCM) of 106 and 111 is 11766.
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 111?
First, calculate the GCD of 106 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 111 = 0 remainder 106 |
| 2 | 111 ÷ 106 = 1 remainder 5 |
| 3 | 106 ÷ 5 = 21 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 170 | 15130 |
| 13 and 13 | 13 |
| 72 and 119 | 8568 |
| 164 and 97 | 15908 |
| 80 and 165 | 2640 |