Least Common Multiple (LCM) of 126 and 109
The least common multiple (LCM) of 126 and 109 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 126 and 109?
First, calculate the GCD of 126 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 109 = 1 remainder 17 |
| 2 | 109 ÷ 17 = 6 remainder 7 |
| 3 | 17 ÷ 7 = 2 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 140 | 420 |
| 196 and 169 | 33124 |
| 12 and 175 | 2100 |
| 160 and 196 | 7840 |
| 109 and 42 | 4578 |