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 |
|---|---|
| 132 and 49 | 6468 |
| 64 and 98 | 3136 |
| 147 and 71 | 10437 |
| 152 and 53 | 8056 |
| 114 and 130 | 7410 |