Least Common Multiple (LCM) of 126 and 67
The least common multiple (LCM) of 126 and 67 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 67?
First, calculate the GCD of 126 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 67 = 1 remainder 59 |
| 2 | 67 ÷ 59 = 1 remainder 8 |
| 3 | 59 ÷ 8 = 7 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 133 | 8778 |
| 90 and 67 | 6030 |
| 51 and 117 | 1989 |
| 107 and 89 | 9523 |
| 40 and 139 | 5560 |