Least Common Multiple (LCM) of 87 and 115
The least common multiple (LCM) of 87 and 115 is 10005.
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 115?
First, calculate the GCD of 87 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 115 = 0 remainder 87 |
| 2 | 115 ÷ 87 = 1 remainder 28 |
| 3 | 87 ÷ 28 = 3 remainder 3 |
| 4 | 28 ÷ 3 = 9 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 140 | 560 |
| 12 and 86 | 516 |
| 102 and 189 | 6426 |
| 119 and 102 | 714 |
| 114 and 182 | 10374 |