Least Common Multiple (LCM) of 192 and 49
The least common multiple (LCM) of 192 and 49 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 192 and 49?
First, calculate the GCD of 192 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 49 = 3 remainder 45 |
| 2 | 49 ÷ 45 = 1 remainder 4 |
| 3 | 45 ÷ 4 = 11 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 102 | 11526 |
| 40 and 31 | 1240 |
| 57 and 178 | 10146 |
| 113 and 32 | 3616 |
| 45 and 24 | 360 |