Least Common Multiple (LCM) of 134 and 165
The least common multiple (LCM) of 134 and 165 is 22110.
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 134 and 165?
First, calculate the GCD of 134 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 165 = 0 remainder 134 |
| 2 | 165 ÷ 134 = 1 remainder 31 |
| 3 | 134 ÷ 31 = 4 remainder 10 |
| 4 | 31 ÷ 10 = 3 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 134 | 6834 |
| 49 and 19 | 931 |
| 173 and 17 | 2941 |
| 144 and 117 | 1872 |
| 65 and 109 | 7085 |