Least Common Multiple (LCM) of 17 and 113
The least common multiple (LCM) of 17 and 113 is 1921.
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 113?
First, calculate the GCD of 17 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 113 = 0 remainder 17 |
| 2 | 113 ÷ 17 = 6 remainder 11 |
| 3 | 17 ÷ 11 = 1 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 160 | 800 |
| 43 and 68 | 2924 |
| 60 and 163 | 9780 |
| 76 and 76 | 76 |
| 106 and 21 | 2226 |