Least Common Multiple (LCM) of 93 and 165
The least common multiple (LCM) of 93 and 165 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 93 and 165?
First, calculate the GCD of 93 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 165 = 0 remainder 93 |
| 2 | 165 ÷ 93 = 1 remainder 72 |
| 3 | 93 ÷ 72 = 1 remainder 21 |
| 4 | 72 ÷ 21 = 3 remainder 9 |
| 5 | 21 ÷ 9 = 2 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 90 | 5490 |
| 43 and 48 | 2064 |
| 48 and 138 | 1104 |
| 48 and 85 | 4080 |
| 147 and 112 | 2352 |