Least Common Multiple (LCM) of 59 and 165
The least common multiple (LCM) of 59 and 165 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 59 and 165?
First, calculate the GCD of 59 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 165 = 0 remainder 59 |
| 2 | 165 ÷ 59 = 2 remainder 47 |
| 3 | 59 ÷ 47 = 1 remainder 12 |
| 4 | 47 ÷ 12 = 3 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 46 | 4554 |
| 123 and 101 | 12423 |
| 177 and 134 | 23718 |
| 46 and 77 | 3542 |
| 188 and 195 | 36660 |