Least Common Multiple (LCM) of 111 and 45
The least common multiple (LCM) of 111 and 45 is 1665.
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 45?
First, calculate the GCD of 111 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 45 = 2 remainder 21 |
| 2 | 45 ÷ 21 = 2 remainder 3 |
| 3 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 15 | 2310 |
| 189 and 197 | 37233 |
| 86 and 92 | 3956 |
| 108 and 89 | 9612 |
| 115 and 14 | 1610 |