Least Common Multiple (LCM) of 87 and 104
The least common multiple (LCM) of 87 and 104 is 9048.
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 104?
First, calculate the GCD of 87 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 104 = 0 remainder 87 |
| 2 | 104 ÷ 87 = 1 remainder 17 |
| 3 | 87 ÷ 17 = 5 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 65 | 3510 |
| 55 and 28 | 1540 |
| 96 and 196 | 4704 |
| 46 and 62 | 1426 |
| 43 and 56 | 2408 |