Least Common Multiple (LCM) of 65 and 168
The least common multiple (LCM) of 65 and 168 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 65 and 168?
First, calculate the GCD of 65 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 168 = 0 remainder 65 |
| 2 | 168 ÷ 65 = 2 remainder 38 |
| 3 | 65 ÷ 38 = 1 remainder 27 |
| 4 | 38 ÷ 27 = 1 remainder 11 |
| 5 | 27 ÷ 11 = 2 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 172 | 10836 |
| 106 and 121 | 12826 |
| 65 and 125 | 1625 |
| 166 and 53 | 8798 |
| 163 and 20 | 3260 |