Least Common Multiple (LCM) of 126 and 159
The least common multiple (LCM) of 126 and 159 is 6678.
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 159?
First, calculate the GCD of 126 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 159 = 0 remainder 126 |
| 2 | 159 ÷ 126 = 1 remainder 33 |
| 3 | 126 ÷ 33 = 3 remainder 27 |
| 4 | 33 ÷ 27 = 1 remainder 6 |
| 5 | 27 ÷ 6 = 4 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 113 | 13108 |
| 155 and 97 | 15035 |
| 71 and 91 | 6461 |
| 181 and 75 | 13575 |
| 32 and 30 | 480 |