Least Common Multiple (LCM) of 199 and 106
The least common multiple (LCM) of 199 and 106 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 199 and 106?
First, calculate the GCD of 199 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 106 = 1 remainder 93 |
| 2 | 106 ÷ 93 = 1 remainder 13 |
| 3 | 93 ÷ 13 = 7 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 195 | 4095 |
| 177 and 17 | 3009 |
| 98 and 188 | 9212 |
| 107 and 110 | 11770 |
| 120 and 56 | 840 |