Least Common Multiple (LCM) of 17 and 97
The least common multiple (LCM) of 17 and 97 is 1649.
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 97?
First, calculate the GCD of 17 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 97 = 0 remainder 17 |
| 2 | 97 ÷ 17 = 5 remainder 12 |
| 3 | 17 ÷ 12 = 1 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 29 | 3422 |
| 63 and 135 | 945 |
| 140 and 41 | 5740 |
| 138 and 178 | 12282 |
| 97 and 109 | 10573 |