Least Common Multiple (LCM) of 126 and 145
The least common multiple (LCM) of 126 and 145 is 18270.
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 145?
First, calculate the GCD of 126 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 145 = 0 remainder 126 |
| 2 | 145 ÷ 126 = 1 remainder 19 |
| 3 | 126 ÷ 19 = 6 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 36 | 1800 |
| 164 and 117 | 19188 |
| 175 and 189 | 4725 |
| 97 and 129 | 12513 |
| 109 and 88 | 9592 |