Least Common Multiple (LCM) of 115 and 165
The least common multiple (LCM) of 115 and 165 is 3795.
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 165?
First, calculate the GCD of 115 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 165 = 0 remainder 115 |
| 2 | 165 ÷ 115 = 1 remainder 50 |
| 3 | 115 ÷ 50 = 2 remainder 15 |
| 4 | 50 ÷ 15 = 3 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 123 | 13530 |
| 185 and 28 | 5180 |
| 33 and 44 | 132 |
| 130 and 180 | 2340 |
| 140 and 24 | 840 |