Least Common Multiple (LCM) of 17 and 101
The least common multiple (LCM) of 17 and 101 is 1717.
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 17 and 101?
First, calculate the GCD of 17 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 101 = 0 remainder 17 |
| 2 | 101 ÷ 17 = 5 remainder 16 |
| 3 | 17 ÷ 16 = 1 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 176 | 34672 |
| 97 and 165 | 16005 |
| 199 and 122 | 24278 |
| 67 and 106 | 7102 |
| 166 and 83 | 166 |