Least Common Multiple (LCM) of 109 and 126
The least common multiple (LCM) of 109 and 126 is 13734.
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 109 and 126?
First, calculate the GCD of 109 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 126 = 0 remainder 109 |
| 2 | 126 ÷ 109 = 1 remainder 17 |
| 3 | 109 ÷ 17 = 6 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 43 | 6063 |
| 198 and 19 | 3762 |
| 30 and 163 | 4890 |
| 167 and 29 | 4843 |
| 171 and 157 | 26847 |