Least Common Multiple (LCM) of 101 and 194
The least common multiple (LCM) of 101 and 194 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 101 and 194?
First, calculate the GCD of 101 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 194 = 0 remainder 101 |
| 2 | 194 ÷ 101 = 1 remainder 93 |
| 3 | 101 ÷ 93 = 1 remainder 8 |
| 4 | 93 ÷ 8 = 11 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 87 | 12354 |
| 55 and 181 | 9955 |
| 45 and 47 | 2115 |
| 89 and 23 | 2047 |
| 116 and 184 | 5336 |