Least Common Multiple (LCM) of 185 and 97
The least common multiple (LCM) of 185 and 97 is 17945.
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 185 and 97?
First, calculate the GCD of 185 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 97 = 1 remainder 88 |
| 2 | 97 ÷ 88 = 1 remainder 9 |
| 3 | 88 ÷ 9 = 9 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 182 | 24934 |
| 40 and 12 | 120 |
| 196 and 175 | 4900 |
| 87 and 66 | 1914 |
| 88 and 46 | 2024 |