Least Common Multiple (LCM) of 107 and 192
The least common multiple (LCM) of 107 and 192 is 20544.
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 107 and 192?
First, calculate the GCD of 107 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 192 = 0 remainder 107 |
| 2 | 192 ÷ 107 = 1 remainder 85 |
| 3 | 107 ÷ 85 = 1 remainder 22 |
| 4 | 85 ÷ 22 = 3 remainder 19 |
| 5 | 22 ÷ 19 = 1 remainder 3 |
| 6 | 19 ÷ 3 = 6 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 77 | 154 |
| 31 and 196 | 6076 |
| 145 and 53 | 7685 |
| 114 and 37 | 4218 |
| 26 and 180 | 2340 |