Least Common Multiple (LCM) of 101 and 193
The least common multiple (LCM) of 101 and 193 is 19493.
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 101 and 193?
First, calculate the GCD of 101 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 193 = 0 remainder 101 |
| 2 | 193 ÷ 101 = 1 remainder 92 |
| 3 | 101 ÷ 92 = 1 remainder 9 |
| 4 | 92 ÷ 9 = 10 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 115 | 12765 |
| 99 and 162 | 1782 |
| 174 and 62 | 5394 |
| 23 and 195 | 4485 |
| 38 and 155 | 5890 |