Least Common Multiple (LCM) of 58 and 165
The least common multiple (LCM) of 58 and 165 is 9570.
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 58 and 165?
First, calculate the GCD of 58 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 165 = 0 remainder 58 |
| 2 | 165 ÷ 58 = 2 remainder 49 |
| 3 | 58 ÷ 49 = 1 remainder 9 |
| 4 | 49 ÷ 9 = 5 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 200 | 20200 |
| 192 and 47 | 9024 |
| 72 and 19 | 1368 |
| 61 and 162 | 9882 |
| 42 and 176 | 3696 |