Least Common Multiple (LCM) of 111 and 114
The least common multiple (LCM) of 111 and 114 is 4218.
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 114?
First, calculate the GCD of 111 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 114 = 0 remainder 111 |
| 2 | 114 ÷ 111 = 1 remainder 3 |
| 3 | 111 ÷ 3 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 89 | 11303 |
| 149 and 92 | 13708 |
| 195 and 135 | 1755 |
| 73 and 200 | 14600 |
| 53 and 70 | 3710 |