Least Common Multiple (LCM) of 66 and 111
The least common multiple (LCM) of 66 and 111 is 2442.
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 111?
First, calculate the GCD of 66 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 111 = 0 remainder 66 |
| 2 | 111 ÷ 66 = 1 remainder 45 |
| 3 | 66 ÷ 45 = 1 remainder 21 |
| 4 | 45 ÷ 21 = 2 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 43 | 4214 |
| 52 and 110 | 2860 |
| 122 and 149 | 18178 |
| 185 and 19 | 3515 |
| 99 and 196 | 19404 |