Least Common Multiple (LCM) of 189 and 87
The least common multiple (LCM) of 189 and 87 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 189 and 87?
First, calculate the GCD of 189 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 87 = 2 remainder 15 |
| 2 | 87 ÷ 15 = 5 remainder 12 |
| 3 | 15 ÷ 12 = 1 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 57 | 4845 |
| 102 and 100 | 5100 |
| 111 and 169 | 18759 |
| 12 and 178 | 1068 |
| 38 and 187 | 7106 |