Least Common Multiple (LCM) of 87 and 193
The least common multiple (LCM) of 87 and 193 is 16791.
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 193?
First, calculate the GCD of 87 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 193 = 0 remainder 87 |
| 2 | 193 ÷ 87 = 2 remainder 19 |
| 3 | 87 ÷ 19 = 4 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 20 | 660 |
| 83 and 43 | 3569 |
| 101 and 86 | 8686 |
| 141 and 15 | 705 |
| 141 and 124 | 17484 |