Least Common Multiple (LCM) of 194 and 106
The least common multiple (LCM) of 194 and 106 is 10282.
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 194 and 106?
First, calculate the GCD of 194 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 106 = 1 remainder 88 |
| 2 | 106 ÷ 88 = 1 remainder 18 |
| 3 | 88 ÷ 18 = 4 remainder 16 |
| 4 | 18 ÷ 16 = 1 remainder 2 |
| 5 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 60 | 1020 |
| 77 and 113 | 8701 |
| 141 and 143 | 20163 |
| 158 and 144 | 11376 |
| 168 and 86 | 7224 |