Least Common Multiple (LCM) of 117 and 165
The least common multiple (LCM) of 117 and 165 is 6435.
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 117 and 165?
First, calculate the GCD of 117 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 165 = 0 remainder 117 |
| 2 | 165 ÷ 117 = 1 remainder 48 |
| 3 | 117 ÷ 48 = 2 remainder 21 |
| 4 | 48 ÷ 21 = 2 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 22 | 682 |
| 47 and 11 | 517 |
| 123 and 54 | 2214 |
| 177 and 196 | 34692 |
| 31 and 182 | 5642 |