Least Common Multiple (LCM) of 194 and 101
The least common multiple (LCM) of 194 and 101 is 19594.
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 101?
First, calculate the GCD of 194 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 101 = 1 remainder 93 |
| 2 | 101 ÷ 93 = 1 remainder 8 |
| 3 | 93 ÷ 8 = 11 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 15 | 2760 |
| 43 and 69 | 2967 |
| 85 and 121 | 10285 |
| 50 and 51 | 2550 |
| 164 and 109 | 17876 |