Least Common Multiple (LCM) of 115 and 17
The least common multiple (LCM) of 115 and 17 is 1955.
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 17?
First, calculate the GCD of 115 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 17 = 6 remainder 13 |
| 2 | 17 ÷ 13 = 1 remainder 4 |
| 3 | 13 ÷ 4 = 3 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 55 | 330 |
| 103 and 108 | 11124 |
| 67 and 107 | 7169 |
| 198 and 112 | 11088 |
| 55 and 110 | 110 |