Least Common Multiple (LCM) of 193 and 101
The least common multiple (LCM) of 193 and 101 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 193 and 101?
First, calculate the GCD of 193 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 101 = 1 remainder 92 |
| 2 | 101 ÷ 92 = 1 remainder 9 |
| 3 | 92 ÷ 9 = 10 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 52 | 104 |
| 64 and 169 | 10816 |
| 131 and 56 | 7336 |
| 64 and 120 | 960 |
| 81 and 52 | 4212 |