Least Common Multiple (LCM) of 126 and 48
The least common multiple (LCM) of 126 and 48 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 126 and 48?
First, calculate the GCD of 126 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 48 = 2 remainder 30 |
| 2 | 48 ÷ 30 = 1 remainder 18 |
| 3 | 30 ÷ 18 = 1 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 97 | 1164 |
| 164 and 69 | 11316 |
| 180 and 57 | 3420 |
| 65 and 149 | 9685 |
| 161 and 128 | 20608 |