Least Common Multiple (LCM) of 126 and 144
The least common multiple (LCM) of 126 and 144 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 144?
First, calculate the GCD of 126 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 144 = 0 remainder 126 |
| 2 | 144 ÷ 126 = 1 remainder 18 |
| 3 | 126 ÷ 18 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 55 | 8195 |
| 138 and 109 | 15042 |
| 148 and 33 | 4884 |
| 60 and 44 | 660 |
| 83 and 109 | 9047 |