Least Common Multiple (LCM) of 126 and 34
The least common multiple (LCM) of 126 and 34 is 2142.
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 34?
First, calculate the GCD of 126 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 34 = 3 remainder 24 |
| 2 | 34 ÷ 24 = 1 remainder 10 |
| 3 | 24 ÷ 10 = 2 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 41 | 5207 |
| 167 and 62 | 10354 |
| 191 and 29 | 5539 |
| 25 and 62 | 1550 |
| 14 and 148 | 1036 |