Least Common Multiple (LCM) of 165 and 97
The least common multiple (LCM) of 165 and 97 is 16005.
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 165 and 97?
First, calculate the GCD of 165 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 97 = 1 remainder 68 |
| 2 | 97 ÷ 68 = 1 remainder 29 |
| 3 | 68 ÷ 29 = 2 remainder 10 |
| 4 | 29 ÷ 10 = 2 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 141 | 7191 |
| 145 and 20 | 580 |
| 48 and 156 | 624 |
| 196 and 185 | 36260 |
| 80 and 30 | 240 |