Least Common Multiple (LCM) of 106 and 193
The least common multiple (LCM) of 106 and 193 is 20458.
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 106 and 193?
First, calculate the GCD of 106 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 193 = 0 remainder 106 |
| 2 | 193 ÷ 106 = 1 remainder 87 |
| 3 | 106 ÷ 87 = 1 remainder 19 |
| 4 | 87 ÷ 19 = 4 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 101 | 4545 |
| 97 and 170 | 16490 |
| 35 and 152 | 5320 |
| 36 and 128 | 1152 |
| 79 and 190 | 15010 |