Least Common Multiple (LCM) of 165 and 67
The least common multiple (LCM) of 165 and 67 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 165 and 67?
First, calculate the GCD of 165 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 67 = 2 remainder 31 |
| 2 | 67 ÷ 31 = 2 remainder 5 |
| 3 | 31 ÷ 5 = 6 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 52 | 1300 |
| 185 and 103 | 19055 |
| 12 and 119 | 1428 |
| 106 and 123 | 13038 |
| 52 and 80 | 1040 |