Least Common Multiple (LCM) of 66 and 115
The least common multiple (LCM) of 66 and 115 is 7590.
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 66 and 115?
First, calculate the GCD of 66 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 115 = 0 remainder 66 |
| 2 | 115 ÷ 66 = 1 remainder 49 |
| 3 | 66 ÷ 49 = 1 remainder 17 |
| 4 | 49 ÷ 17 = 2 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 126 | 8064 |
| 189 and 176 | 33264 |
| 155 and 22 | 3410 |
| 25 and 48 | 1200 |
| 181 and 61 | 11041 |