Least Common Multiple (LCM) of 106 and 199
The least common multiple (LCM) of 106 and 199 is 21094.
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 199?
First, calculate the GCD of 106 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 199 = 0 remainder 106 |
| 2 | 199 ÷ 106 = 1 remainder 93 |
| 3 | 106 ÷ 93 = 1 remainder 13 |
| 4 | 93 ÷ 13 = 7 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 106 | 5830 |
| 57 and 10 | 570 |
| 89 and 132 | 11748 |
| 170 and 166 | 14110 |
| 107 and 30 | 3210 |