Least Common Multiple (LCM) of 20 and 192
The least common multiple (LCM) of 20 and 192 is 960.
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 20 and 192?
First, calculate the GCD of 20 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 192 = 0 remainder 20 |
| 2 | 192 ÷ 20 = 9 remainder 12 |
| 3 | 20 ÷ 12 = 1 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 66 | 1584 |
| 194 and 135 | 26190 |
| 23 and 51 | 1173 |
| 31 and 133 | 4123 |
| 106 and 159 | 318 |