Least Common Multiple (LCM) of 126 and 165
The least common multiple (LCM) of 126 and 165 is 6930.
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 165?
First, calculate the GCD of 126 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 165 = 0 remainder 126 |
| 2 | 165 ÷ 126 = 1 remainder 39 |
| 3 | 126 ÷ 39 = 3 remainder 9 |
| 4 | 39 ÷ 9 = 4 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 24 | 504 |
| 86 and 63 | 5418 |
| 160 and 84 | 3360 |
| 118 and 27 | 3186 |
| 199 and 21 | 4179 |