Least Common Multiple (LCM) of 72 and 193
The least common multiple (LCM) of 72 and 193 is 13896.
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 72 and 193?
First, calculate the GCD of 72 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 193 = 0 remainder 72 |
| 2 | 193 ÷ 72 = 2 remainder 49 |
| 3 | 72 ÷ 49 = 1 remainder 23 |
| 4 | 49 ÷ 23 = 2 remainder 3 |
| 5 | 23 ÷ 3 = 7 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 167 | 31563 |
| 130 and 98 | 6370 |
| 107 and 41 | 4387 |
| 103 and 196 | 20188 |
| 145 and 38 | 5510 |