Least Common Multiple (LCM) of 18 and 68
The least common multiple (LCM) of 18 and 68 is 612.
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 18 and 68?
First, calculate the GCD of 18 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 68 = 0 remainder 18 |
| 2 | 68 ÷ 18 = 3 remainder 14 |
| 3 | 18 ÷ 14 = 1 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 124 | 1240 |
| 198 and 181 | 35838 |
| 102 and 147 | 4998 |
| 39 and 167 | 6513 |
| 65 and 17 | 1105 |