Least Common Multiple (LCM) of 87 and 189
The least common multiple (LCM) of 87 and 189 is 5481.
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 189?
First, calculate the GCD of 87 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 189 = 0 remainder 87 |
| 2 | 189 ÷ 87 = 2 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 |
|---|---|
| 152 and 179 | 27208 |
| 99 and 49 | 4851 |
| 159 and 124 | 19716 |
| 165 and 102 | 5610 |
| 35 and 75 | 525 |