Least Common Multiple (LCM) of 97 and 165
The least common multiple (LCM) of 97 and 165 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 97 and 165?
First, calculate the GCD of 97 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 165 = 0 remainder 97 |
| 2 | 165 ÷ 97 = 1 remainder 68 |
| 3 | 97 ÷ 68 = 1 remainder 29 |
| 4 | 68 ÷ 29 = 2 remainder 10 |
| 5 | 29 ÷ 10 = 2 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 65 | 715 |
| 170 and 151 | 25670 |
| 150 and 190 | 2850 |
| 160 and 26 | 2080 |
| 127 and 199 | 25273 |