Least Common Multiple (LCM) of 87 and 71
The least common multiple (LCM) of 87 and 71 is 6177.
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 71?
First, calculate the GCD of 87 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 71 = 1 remainder 16 |
| 2 | 71 ÷ 16 = 4 remainder 7 |
| 3 | 16 ÷ 7 = 2 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 109 | 18966 |
| 136 and 11 | 1496 |
| 199 and 146 | 29054 |
| 89 and 20 | 1780 |
| 158 and 62 | 4898 |