Least Common Multiple (LCM) of 193 and 71
The least common multiple (LCM) of 193 and 71 is 13703.
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 71?
First, calculate the GCD of 193 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 71 = 2 remainder 51 |
| 2 | 71 ÷ 51 = 1 remainder 20 |
| 3 | 51 ÷ 20 = 2 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 119 | 1428 |
| 129 and 162 | 6966 |
| 183 and 23 | 4209 |
| 114 and 41 | 4674 |
| 15 and 20 | 60 |