Least Common Multiple (LCM) of 113 and 192
The least common multiple (LCM) of 113 and 192 is 21696.
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 113 and 192?
First, calculate the GCD of 113 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 192 = 0 remainder 113 |
| 2 | 192 ÷ 113 = 1 remainder 79 |
| 3 | 113 ÷ 79 = 1 remainder 34 |
| 4 | 79 ÷ 34 = 2 remainder 11 |
| 5 | 34 ÷ 11 = 3 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 16 | 240 |
| 38 and 112 | 2128 |
| 197 and 171 | 33687 |
| 83 and 180 | 14940 |
| 77 and 164 | 12628 |