Least Common Multiple (LCM) of 64 and 189
The least common multiple (LCM) of 64 and 189 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 64 and 189?
First, calculate the GCD of 64 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 189 = 0 remainder 64 |
| 2 | 189 ÷ 64 = 2 remainder 61 |
| 3 | 64 ÷ 61 = 1 remainder 3 |
| 4 | 61 ÷ 3 = 20 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 23 | 2461 |
| 71 and 140 | 9940 |
| 44 and 40 | 440 |
| 171 and 88 | 15048 |
| 162 and 150 | 4050 |