Least Common Multiple (LCM) of 73 and 165
The least common multiple (LCM) of 73 and 165 is 12045.
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 73 and 165?
First, calculate the GCD of 73 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 165 = 0 remainder 73 |
| 2 | 165 ÷ 73 = 2 remainder 19 |
| 3 | 73 ÷ 19 = 3 remainder 16 |
| 4 | 19 ÷ 16 = 1 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 34 | 2074 |
| 84 and 65 | 5460 |
| 30 and 55 | 330 |
| 98 and 144 | 7056 |
| 97 and 167 | 16199 |