Least Common Multiple (LCM) of 69 and 193
The least common multiple (LCM) of 69 and 193 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 69 and 193?
First, calculate the GCD of 69 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 193 = 0 remainder 69 |
| 2 | 193 ÷ 69 = 2 remainder 55 |
| 3 | 69 ÷ 55 = 1 remainder 14 |
| 4 | 55 ÷ 14 = 3 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 170 | 3570 |
| 68 and 184 | 3128 |
| 40 and 176 | 880 |
| 13 and 133 | 1729 |
| 179 and 196 | 35084 |