Least Common Multiple (LCM) of 14 and 68
The least common multiple (LCM) of 14 and 68 is 476.
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 14 and 68?
First, calculate the GCD of 14 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 68 = 0 remainder 14 |
| 2 | 68 ÷ 14 = 4 remainder 12 |
| 3 | 14 ÷ 12 = 1 remainder 2 |
| 4 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 200 | 8200 |
| 166 and 72 | 5976 |
| 52 and 19 | 988 |
| 14 and 176 | 1232 |
| 69 and 18 | 414 |