Least Common Multiple (LCM) of 193 and 100
The least common multiple (LCM) of 193 and 100 is 19300.
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 100?
First, calculate the GCD of 193 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 100 = 1 remainder 93 |
| 2 | 100 ÷ 93 = 1 remainder 7 |
| 3 | 93 ÷ 7 = 13 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 11 | 1287 |
| 137 and 68 | 9316 |
| 72 and 49 | 3528 |
| 18 and 23 | 414 |
| 14 and 131 | 1834 |