Least Common Multiple (LCM) of 87 and 185
The least common multiple (LCM) of 87 and 185 is 16095.
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 185?
First, calculate the GCD of 87 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 185 = 0 remainder 87 |
| 2 | 185 ÷ 87 = 2 remainder 11 |
| 3 | 87 ÷ 11 = 7 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 80 | 160 |
| 49 and 30 | 1470 |
| 40 and 12 | 120 |
| 131 and 66 | 8646 |
| 84 and 71 | 5964 |