Least Common Multiple (LCM) of 45 and 165
The least common multiple (LCM) of 45 and 165 is 495.
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 45 and 165?
First, calculate the GCD of 45 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 165 = 0 remainder 45 |
| 2 | 165 ÷ 45 = 3 remainder 30 |
| 3 | 45 ÷ 30 = 1 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 42 | 294 |
| 123 and 33 | 1353 |
| 66 and 104 | 3432 |
| 192 and 27 | 1728 |
| 99 and 119 | 11781 |