Least Common Multiple (LCM) of 12 and 126
The least common multiple (LCM) of 12 and 126 is 252.
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 12 and 126?
First, calculate the GCD of 12 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 126 = 0 remainder 12 |
| 2 | 126 ÷ 12 = 10 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 172 | 32508 |
| 25 and 51 | 1275 |
| 79 and 101 | 7979 |
| 54 and 115 | 6210 |
| 108 and 24 | 216 |