Least Common Multiple (LCM) of 87 and 102
The least common multiple (LCM) of 87 and 102 is 2958.
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 102?
First, calculate the GCD of 87 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 102 = 0 remainder 87 |
| 2 | 102 ÷ 87 = 1 remainder 15 |
| 3 | 87 ÷ 15 = 5 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 15 | 555 |
| 76 and 183 | 13908 |
| 126 and 17 | 2142 |
| 101 and 194 | 19594 |
| 67 and 111 | 7437 |