Least Common Multiple (LCM) of 126 and 54
The least common multiple (LCM) of 126 and 54 is 378.
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 54?
First, calculate the GCD of 126 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 54 = 2 remainder 18 |
| 2 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 67 | 9849 |
| 180 and 174 | 5220 |
| 47 and 153 | 7191 |
| 138 and 106 | 7314 |
| 80 and 17 | 1360 |