Least Common Multiple (LCM) of 192 and 113
The least common multiple (LCM) of 192 and 113 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 192 and 113?
First, calculate the GCD of 192 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 113 = 1 remainder 79 |
| 2 | 113 ÷ 79 = 1 remainder 34 |
| 3 | 79 ÷ 34 = 2 remainder 11 |
| 4 | 34 ÷ 11 = 3 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 18 | 1710 |
| 85 and 31 | 2635 |
| 123 and 163 | 20049 |
| 77 and 142 | 10934 |
| 97 and 146 | 14162 |