Least Common Multiple (LCM) of 193 and 113
The least common multiple (LCM) of 193 and 113 is 21809.
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 113?
First, calculate the GCD of 193 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 113 = 1 remainder 80 |
| 2 | 113 ÷ 80 = 1 remainder 33 |
| 3 | 80 ÷ 33 = 2 remainder 14 |
| 4 | 33 ÷ 14 = 2 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 69 | 2208 |
| 106 and 99 | 10494 |
| 70 and 61 | 4270 |
| 80 and 127 | 10160 |
| 129 and 47 | 6063 |