Least Common Multiple (LCM) of 15 and 193
The least common multiple (LCM) of 15 and 193 is 2895.
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 15 and 193?
First, calculate the GCD of 15 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 193 = 0 remainder 15 |
| 2 | 193 ÷ 15 = 12 remainder 13 |
| 3 | 15 ÷ 13 = 1 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 166 | 17430 |
| 36 and 176 | 1584 |
| 78 and 174 | 2262 |
| 81 and 64 | 5184 |
| 106 and 31 | 3286 |