Least Common Multiple (LCM) of 103 and 96
The least common multiple (LCM) of 103 and 96 is 9888.
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 103 and 96?
First, calculate the GCD of 103 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 96 = 1 remainder 7 |
| 2 | 96 ÷ 7 = 13 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 174 | 6438 |
| 125 and 123 | 15375 |
| 164 and 184 | 7544 |
| 184 and 197 | 36248 |
| 165 and 169 | 27885 |