Least Common Multiple (LCM) of 126 and 65
The least common multiple (LCM) of 126 and 65 is 8190.
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 65?
First, calculate the GCD of 126 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 65 = 1 remainder 61 |
| 2 | 65 ÷ 61 = 1 remainder 4 |
| 3 | 61 ÷ 4 = 15 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 45 | 360 |
| 96 and 186 | 2976 |
| 87 and 86 | 7482 |
| 150 and 166 | 12450 |
| 28 and 142 | 1988 |