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 |
|---|---|
| 16 and 12 | 48 |
| 117 and 119 | 13923 |
| 134 and 101 | 13534 |
| 64 and 173 | 11072 |
| 175 and 75 | 525 |