Least Common Multiple (LCM) of 48 and 126
The least common multiple (LCM) of 48 and 126 is 1008.
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 48 and 126?
First, calculate the GCD of 48 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 126 = 0 remainder 48 |
| 2 | 126 ÷ 48 = 2 remainder 30 |
| 3 | 48 ÷ 30 = 1 remainder 18 |
| 4 | 30 ÷ 18 = 1 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 178 | 2670 |
| 18 and 27 | 54 |
| 154 and 30 | 2310 |
| 177 and 67 | 11859 |
| 177 and 101 | 17877 |