Least Common Multiple (LCM) of 140 and 192
The least common multiple (LCM) of 140 and 192 is 6720.
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 140 and 192?
First, calculate the GCD of 140 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 192 = 0 remainder 140 |
| 2 | 192 ÷ 140 = 1 remainder 52 |
| 3 | 140 ÷ 52 = 2 remainder 36 |
| 4 | 52 ÷ 36 = 1 remainder 16 |
| 5 | 36 ÷ 16 = 2 remainder 4 |
| 6 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 189 | 3024 |
| 115 and 173 | 19895 |
| 19 and 199 | 3781 |
| 92 and 124 | 2852 |
| 124 and 92 | 2852 |