Least Common Multiple (LCM) of 142 and 192
The least common multiple (LCM) of 142 and 192 is 13632.
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 142 and 192?
First, calculate the GCD of 142 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 192 = 0 remainder 142 |
| 2 | 192 ÷ 142 = 1 remainder 50 |
| 3 | 142 ÷ 50 = 2 remainder 42 |
| 4 | 50 ÷ 42 = 1 remainder 8 |
| 5 | 42 ÷ 8 = 5 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 57 | 6042 |
| 96 and 35 | 3360 |
| 14 and 127 | 1778 |
| 33 and 91 | 3003 |
| 41 and 126 | 5166 |