Least Common Multiple (LCM) of 105 and 92
The least common multiple (LCM) of 105 and 92 is 9660.
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 105 and 92?
First, calculate the GCD of 105 and 92 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 92 = 1 remainder 13 |
| 2 | 92 ÷ 13 = 7 remainder 1 |
| 3 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 53 | 7049 |
| 58 and 199 | 11542 |
| 129 and 61 | 7869 |
| 49 and 129 | 6321 |
| 101 and 130 | 13130 |