Least Common Multiple (LCM) of 97 and 170
The least common multiple (LCM) of 97 and 170 is 16490.
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 97 and 170?
First, calculate the GCD of 97 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 170 = 0 remainder 97 |
| 2 | 170 ÷ 97 = 1 remainder 73 |
| 3 | 97 ÷ 73 = 1 remainder 24 |
| 4 | 73 ÷ 24 = 3 remainder 1 |
| 5 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 190 | 1710 |
| 49 and 162 | 7938 |
| 108 and 59 | 6372 |
| 21 and 165 | 1155 |
| 180 and 144 | 720 |