Least Common Multiple (LCM) of 87 and 194
The least common multiple (LCM) of 87 and 194 is 16878.
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 87 and 194?
First, calculate the GCD of 87 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 194 = 0 remainder 87 |
| 2 | 194 ÷ 87 = 2 remainder 20 |
| 3 | 87 ÷ 20 = 4 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 54 | 2538 |
| 117 and 180 | 2340 |
| 159 and 125 | 19875 |
| 108 and 199 | 21492 |
| 78 and 65 | 390 |