Least Common Multiple (LCM) of 87 and 105
The least common multiple (LCM) of 87 and 105 is 3045.
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 105?
First, calculate the GCD of 87 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 105 = 0 remainder 87 |
| 2 | 105 ÷ 87 = 1 remainder 18 |
| 3 | 87 ÷ 18 = 4 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 113 | 11526 |
| 142 and 72 | 5112 |
| 187 and 131 | 24497 |
| 187 and 148 | 27676 |
| 111 and 59 | 6549 |