Least Common Multiple (LCM) of 126 and 111
The least common multiple (LCM) of 126 and 111 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 126 and 111?
First, calculate the GCD of 126 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 111 = 1 remainder 15 |
| 2 | 111 ÷ 15 = 7 remainder 6 |
| 3 | 15 ÷ 6 = 2 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 44 | 3124 |
| 198 and 171 | 3762 |
| 172 and 40 | 1720 |
| 114 and 41 | 4674 |
| 38 and 126 | 2394 |