Least Common Multiple (LCM) of 165 and 61
The least common multiple (LCM) of 165 and 61 is 10065.
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 61?
First, calculate the GCD of 165 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 61 = 2 remainder 43 |
| 2 | 61 ÷ 43 = 1 remainder 18 |
| 3 | 43 ÷ 18 = 2 remainder 7 |
| 4 | 18 ÷ 7 = 2 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 26 | 2314 |
| 189 and 134 | 25326 |
| 105 and 123 | 4305 |
| 117 and 119 | 13923 |
| 41 and 148 | 6068 |