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 |
|---|---|
| 121 and 113 | 13673 |
| 107 and 160 | 17120 |
| 124 and 55 | 6820 |
| 28 and 67 | 1876 |
| 146 and 51 | 7446 |