Least Common Multiple (LCM) of 68 and 165
The least common multiple (LCM) of 68 and 165 is 11220.
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 68 and 165?
First, calculate the GCD of 68 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 165 = 0 remainder 68 |
| 2 | 165 ÷ 68 = 2 remainder 29 |
| 3 | 68 ÷ 29 = 2 remainder 10 |
| 4 | 29 ÷ 10 = 2 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 162 | 13284 |
| 81 and 185 | 14985 |
| 135 and 117 | 1755 |
| 105 and 124 | 13020 |
| 33 and 156 | 1716 |