Least Common Multiple (LCM) of 111 and 126
The least common multiple (LCM) of 111 and 126 is 4662.
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 126?
First, calculate the GCD of 111 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 126 = 0 remainder 111 |
| 2 | 126 ÷ 111 = 1 remainder 15 |
| 3 | 111 ÷ 15 = 7 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 143 | 16302 |
| 24 and 195 | 1560 |
| 185 and 85 | 3145 |
| 10 and 131 | 1310 |
| 168 and 116 | 4872 |