Least Common Multiple (LCM) of 67 and 165
The least common multiple (LCM) of 67 and 165 is 11055.
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 67 and 165?
First, calculate the GCD of 67 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 165 = 0 remainder 67 |
| 2 | 165 ÷ 67 = 2 remainder 31 |
| 3 | 67 ÷ 31 = 2 remainder 5 |
| 4 | 31 ÷ 5 = 6 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 135 | 540 |
| 11 and 23 | 253 |
| 104 and 91 | 728 |
| 181 and 50 | 9050 |
| 157 and 36 | 5652 |