Least Common Multiple (LCM) of 42 and 192
The least common multiple (LCM) of 42 and 192 is 1344.
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 42 and 192?
First, calculate the GCD of 42 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 192 = 0 remainder 42 |
| 2 | 192 ÷ 42 = 4 remainder 24 |
| 3 | 42 ÷ 24 = 1 remainder 18 |
| 4 | 24 ÷ 18 = 1 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 197 | 33687 |
| 187 and 32 | 5984 |
| 119 and 18 | 2142 |
| 121 and 104 | 12584 |
| 27 and 19 | 513 |