Least Common Multiple (LCM) of 115 and 66
The least common multiple (LCM) of 115 and 66 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 115 and 66?
First, calculate the GCD of 115 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 66 = 1 remainder 49 |
| 2 | 66 ÷ 49 = 1 remainder 17 |
| 3 | 49 ÷ 17 = 2 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 144 | 15408 |
| 27 and 99 | 297 |
| 43 and 107 | 4601 |
| 118 and 165 | 19470 |
| 61 and 31 | 1891 |