Least Common Multiple (LCM) of 109 and 66
The least common multiple (LCM) of 109 and 66 is 7194.
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 109 and 66?
First, calculate the GCD of 109 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 66 = 1 remainder 43 |
| 2 | 66 ÷ 43 = 1 remainder 23 |
| 3 | 43 ÷ 23 = 1 remainder 20 |
| 4 | 23 ÷ 20 = 1 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 108 | 540 |
| 195 and 21 | 1365 |
| 82 and 184 | 7544 |
| 61 and 106 | 6466 |
| 41 and 97 | 3977 |