Least Common Multiple (LCM) of 87 and 117
The least common multiple (LCM) of 87 and 117 is 3393.
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 117?
First, calculate the GCD of 87 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 117 = 0 remainder 87 |
| 2 | 117 ÷ 87 = 1 remainder 30 |
| 3 | 87 ÷ 30 = 2 remainder 27 |
| 4 | 30 ÷ 27 = 1 remainder 3 |
| 5 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 81 | 81 |
| 182 and 152 | 13832 |
| 27 and 152 | 4104 |
| 114 and 156 | 2964 |
| 28 and 78 | 1092 |