Least Common Multiple (LCM) of 22 and 192
The least common multiple (LCM) of 22 and 192 is 2112.
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 192?
First, calculate the GCD of 22 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 192 = 0 remainder 22 |
| 2 | 192 ÷ 22 = 8 remainder 16 |
| 3 | 22 ÷ 16 = 1 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 59 | 10384 |
| 132 and 138 | 3036 |
| 137 and 101 | 13837 |
| 34 and 10 | 170 |
| 130 and 97 | 12610 |