Least Common Multiple (LCM) of 105 and 96
The least common multiple (LCM) of 105 and 96 is 3360.
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 96?
First, calculate the GCD of 105 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 96 = 1 remainder 9 |
| 2 | 96 ÷ 9 = 10 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 187 | 12903 |
| 74 and 194 | 7178 |
| 52 and 169 | 676 |
| 101 and 172 | 17372 |
| 110 and 74 | 4070 |