Least Common Multiple (LCM) of 126 and 143
The least common multiple (LCM) of 126 and 143 is 18018.
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 143?
First, calculate the GCD of 126 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 143 = 0 remainder 126 |
| 2 | 143 ÷ 126 = 1 remainder 17 |
| 3 | 126 ÷ 17 = 7 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 105 | 14070 |
| 123 and 74 | 9102 |
| 57 and 60 | 1140 |
| 12 and 171 | 684 |
| 190 and 144 | 13680 |