Least Common Multiple (LCM) of 193 and 69
The least common multiple (LCM) of 193 and 69 is 13317.
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 193 and 69?
First, calculate the GCD of 193 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 69 = 2 remainder 55 |
| 2 | 69 ÷ 55 = 1 remainder 14 |
| 3 | 55 ÷ 14 = 3 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 25 | 1975 |
| 105 and 173 | 18165 |
| 192 and 136 | 3264 |
| 144 and 21 | 1008 |
| 21 and 57 | 399 |