Least Common Multiple (LCM) of 165 and 133
The least common multiple (LCM) of 165 and 133 is 21945.
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 133?
First, calculate the GCD of 165 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 133 = 1 remainder 32 |
| 2 | 133 ÷ 32 = 4 remainder 5 |
| 3 | 32 ÷ 5 = 6 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 123 | 16113 |
| 128 and 48 | 384 |
| 115 and 79 | 9085 |
| 93 and 155 | 465 |
| 95 and 12 | 1140 |