Least Common Multiple (LCM) of 50 and 192
The least common multiple (LCM) of 50 and 192 is 4800.
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 50 and 192?
First, calculate the GCD of 50 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 192 = 0 remainder 50 |
| 2 | 192 ÷ 50 = 3 remainder 42 |
| 3 | 50 ÷ 42 = 1 remainder 8 |
| 4 | 42 ÷ 8 = 5 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 109 | 14715 |
| 105 and 52 | 5460 |
| 55 and 176 | 880 |
| 12 and 77 | 924 |
| 41 and 180 | 7380 |