Least Common Multiple (LCM) of 192 and 20
The least common multiple (LCM) of 192 and 20 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 192 and 20?
First, calculate the GCD of 192 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 20 = 9 remainder 12 |
| 2 | 20 ÷ 12 = 1 remainder 8 |
| 3 | 12 ÷ 8 = 1 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 74 | 14578 |
| 143 and 11 | 143 |
| 10 and 108 | 540 |
| 96 and 173 | 16608 |
| 107 and 152 | 16264 |