Least Common Multiple (LCM) of 165 and 73
The least common multiple (LCM) of 165 and 73 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 165 and 73?
First, calculate the GCD of 165 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 73 = 2 remainder 19 |
| 2 | 73 ÷ 19 = 3 remainder 16 |
| 3 | 19 ÷ 16 = 1 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 194 | 3298 |
| 152 and 106 | 8056 |
| 192 and 44 | 2112 |
| 140 and 173 | 24220 |
| 40 and 177 | 7080 |