Least Common Multiple (LCM) of 54 and 126
The least common multiple (LCM) of 54 and 126 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 54 and 126?
First, calculate the GCD of 54 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 126 = 0 remainder 54 |
| 2 | 126 ÷ 54 = 2 remainder 18 |
| 3 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 147 | 6027 |
| 35 and 38 | 1330 |
| 49 and 43 | 2107 |
| 120 and 193 | 23160 |
| 129 and 189 | 8127 |