Least Common Multiple (LCM) of 126 and 134
The least common multiple (LCM) of 126 and 134 is 8442.
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 134?
First, calculate the GCD of 126 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 134 = 0 remainder 126 |
| 2 | 134 ÷ 126 = 1 remainder 8 |
| 3 | 126 ÷ 8 = 15 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 124 | 1860 |
| 114 and 12 | 228 |
| 146 and 109 | 15914 |
| 19 and 156 | 2964 |
| 40 and 28 | 280 |