Least Common Multiple (LCM) of 22 and 144
The least common multiple (LCM) of 22 and 144 is 1584.
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 22 and 144?
First, calculate the GCD of 22 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 144 = 0 remainder 22 |
| 2 | 144 ÷ 22 = 6 remainder 12 |
| 3 | 22 ÷ 12 = 1 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 135 | 5940 |
| 155 and 57 | 8835 |
| 80 and 154 | 6160 |
| 180 and 18 | 180 |
| 46 and 23 | 46 |