Least Common Multiple (LCM) of 165 and 59
The least common multiple (LCM) of 165 and 59 is 9735.
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 59?
First, calculate the GCD of 165 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 59 = 2 remainder 47 |
| 2 | 59 ÷ 47 = 1 remainder 12 |
| 3 | 47 ÷ 12 = 3 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 99 | 8811 |
| 189 and 29 | 5481 |
| 107 and 108 | 11556 |
| 15 and 187 | 2805 |
| 121 and 156 | 18876 |