Least Common Multiple (LCM) of 165 and 93
The least common multiple (LCM) of 165 and 93 is 5115.
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 93?
First, calculate the GCD of 165 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 93 = 1 remainder 72 |
| 2 | 93 ÷ 72 = 1 remainder 21 |
| 3 | 72 ÷ 21 = 3 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 10 | 210 |
| 127 and 29 | 3683 |
| 33 and 16 | 528 |
| 198 and 21 | 1386 |
| 159 and 46 | 7314 |