Least Common Multiple (LCM) of 66 and 107
The least common multiple (LCM) of 66 and 107 is 7062.
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 107?
First, calculate the GCD of 66 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 107 = 0 remainder 66 |
| 2 | 107 ÷ 66 = 1 remainder 41 |
| 3 | 66 ÷ 41 = 1 remainder 25 |
| 4 | 41 ÷ 25 = 1 remainder 16 |
| 5 | 25 ÷ 16 = 1 remainder 9 |
| 6 | 16 ÷ 9 = 1 remainder 7 |
| 7 | 9 ÷ 7 = 1 remainder 2 |
| 8 | 7 ÷ 2 = 3 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 155 | 30070 |
| 200 and 21 | 4200 |
| 165 and 112 | 18480 |
| 131 and 138 | 18078 |
| 149 and 172 | 25628 |