Least Common Multiple (LCM) of 66 and 109
The least common multiple (LCM) of 66 and 109 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 66 and 109?
First, calculate the GCD of 66 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 109 = 0 remainder 66 |
| 2 | 109 ÷ 66 = 1 remainder 43 |
| 3 | 66 ÷ 43 = 1 remainder 23 |
| 4 | 43 ÷ 23 = 1 remainder 20 |
| 5 | 23 ÷ 20 = 1 remainder 3 |
| 6 | 20 ÷ 3 = 6 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 161 | 21896 |
| 91 and 104 | 728 |
| 93 and 169 | 15717 |
| 157 and 187 | 29359 |
| 190 and 103 | 19570 |