Least Common Multiple (LCM) of 192 and 42
The least common multiple (LCM) of 192 and 42 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 192 and 42?
First, calculate the GCD of 192 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 42 = 4 remainder 24 |
| 2 | 42 ÷ 24 = 1 remainder 18 |
| 3 | 24 ÷ 18 = 1 remainder 6 |
| 4 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 126 | 126 |
| 189 and 71 | 13419 |
| 21 and 20 | 420 |
| 176 and 78 | 6864 |
| 38 and 116 | 2204 |