Least Common Multiple (LCM) of 111 and 66
The least common multiple (LCM) of 111 and 66 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 111 and 66?
First, calculate the GCD of 111 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 66 = 1 remainder 45 |
| 2 | 66 ÷ 45 = 1 remainder 21 |
| 3 | 45 ÷ 21 = 2 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 162 | 3078 |
| 163 and 101 | 16463 |
| 166 and 108 | 8964 |
| 123 and 102 | 4182 |
| 11 and 16 | 176 |