Least Common Multiple (LCM) of 67 and 126
The least common multiple (LCM) of 67 and 126 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 67 and 126?
First, calculate the GCD of 67 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 126 = 0 remainder 67 |
| 2 | 126 ÷ 67 = 1 remainder 59 |
| 3 | 67 ÷ 59 = 1 remainder 8 |
| 4 | 59 ÷ 8 = 7 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 177 | 10797 |
| 127 and 34 | 4318 |
| 73 and 19 | 1387 |
| 33 and 68 | 2244 |
| 149 and 86 | 12814 |