Least Common Multiple (LCM) of 111 and 75
The least common multiple (LCM) of 111 and 75 is 2775.
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 75?
First, calculate the GCD of 111 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 75 = 1 remainder 36 |
| 2 | 75 ÷ 36 = 2 remainder 3 |
| 3 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 157 | 24178 |
| 189 and 163 | 30807 |
| 125 and 83 | 10375 |
| 18 and 15 | 90 |
| 162 and 193 | 31266 |