Least Common Multiple (LCM) of 34 and 165
The least common multiple (LCM) of 34 and 165 is 5610.
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 34 and 165?
First, calculate the GCD of 34 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 165 = 0 remainder 34 |
| 2 | 165 ÷ 34 = 4 remainder 29 |
| 3 | 34 ÷ 29 = 1 remainder 5 |
| 4 | 29 ÷ 5 = 5 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 30 | 4710 |
| 120 and 167 | 20040 |
| 21 and 30 | 210 |
| 12 and 127 | 1524 |
| 149 and 17 | 2533 |