Least Common Multiple (LCM) of 168 and 65
The least common multiple (LCM) of 168 and 65 is 10920.
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 168 and 65?
First, calculate the GCD of 168 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 65 = 2 remainder 38 |
| 2 | 65 ÷ 38 = 1 remainder 27 |
| 3 | 38 ÷ 27 = 1 remainder 11 |
| 4 | 27 ÷ 11 = 2 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 174 | 3306 |
| 96 and 141 | 4512 |
| 77 and 80 | 6160 |
| 90 and 140 | 1260 |
| 15 and 16 | 240 |