Least Common Multiple (LCM) of 165 and 52
The least common multiple (LCM) of 165 and 52 is 8580.
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 52?
First, calculate the GCD of 165 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 52 = 3 remainder 9 |
| 2 | 52 ÷ 9 = 5 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 115 | 22080 |
| 111 and 10 | 1110 |
| 153 and 75 | 3825 |
| 32 and 21 | 672 |
| 52 and 133 | 6916 |