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 |
|---|---|
| 52 and 108 | 1404 |
| 27 and 122 | 3294 |
| 97 and 154 | 14938 |
| 186 and 137 | 25482 |
| 177 and 145 | 25665 |