Least Common Multiple (LCM) of 11 and 111
The least common multiple (LCM) of 11 and 111 is 1221.
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 11 and 111?
First, calculate the GCD of 11 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 111 = 0 remainder 11 |
| 2 | 111 ÷ 11 = 10 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 23 | 1541 |
| 28 and 199 | 5572 |
| 37 and 57 | 2109 |
| 192 and 74 | 7104 |
| 171 and 75 | 4275 |