Least Common Multiple (LCM) of 97 and 189
The least common multiple (LCM) of 97 and 189 is 18333.
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 189?
First, calculate the GCD of 97 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 189 = 0 remainder 97 |
| 2 | 189 ÷ 97 = 1 remainder 92 |
| 3 | 97 ÷ 92 = 1 remainder 5 |
| 4 | 92 ÷ 5 = 18 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 170 | 9010 |
| 172 and 166 | 14276 |
| 77 and 102 | 7854 |
| 31 and 82 | 2542 |
| 114 and 140 | 7980 |