Least Common Multiple (LCM) of 189 and 64
The least common multiple (LCM) of 189 and 64 is 12096.
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 64?
First, calculate the GCD of 189 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 64 = 2 remainder 61 |
| 2 | 64 ÷ 61 = 1 remainder 3 |
| 3 | 61 ÷ 3 = 20 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 28 | 3108 |
| 111 and 146 | 16206 |
| 84 and 67 | 5628 |
| 140 and 185 | 5180 |
| 175 and 42 | 1050 |