Least Common Multiple (LCM) of 199 and 87
The least common multiple (LCM) of 199 and 87 is 17313.
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 199 and 87?
First, calculate the GCD of 199 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 87 = 2 remainder 25 |
| 2 | 87 ÷ 25 = 3 remainder 12 |
| 3 | 25 ÷ 12 = 2 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 171 | 1710 |
| 60 and 129 | 2580 |
| 120 and 83 | 9960 |
| 49 and 163 | 7987 |
| 167 and 42 | 7014 |