Least Common Multiple (LCM) of 102 and 111
The least common multiple (LCM) of 102 and 111 is 3774.
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 102 and 111?
First, calculate the GCD of 102 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 111 = 0 remainder 102 |
| 2 | 111 ÷ 102 = 1 remainder 9 |
| 3 | 102 ÷ 9 = 11 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 119 | 19873 |
| 162 and 180 | 1620 |
| 50 and 18 | 450 |
| 199 and 59 | 11741 |
| 34 and 24 | 408 |