Least Common Multiple (LCM) of 49 and 192
The least common multiple (LCM) of 49 and 192 is 9408.
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 49 and 192?
First, calculate the GCD of 49 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 192 = 0 remainder 49 |
| 2 | 192 ÷ 49 = 3 remainder 45 |
| 3 | 49 ÷ 45 = 1 remainder 4 |
| 4 | 45 ÷ 4 = 11 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 166 | 13446 |
| 188 and 195 | 36660 |
| 95 and 48 | 4560 |
| 114 and 135 | 5130 |
| 58 and 122 | 3538 |