Least Common Multiple (LCM) of 14 and 108
The least common multiple (LCM) of 14 and 108 is 756.
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 108?
First, calculate the GCD of 14 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 108 = 0 remainder 14 |
| 2 | 108 ÷ 14 = 7 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 29 | 5075 |
| 200 and 129 | 25800 |
| 188 and 121 | 22748 |
| 95 and 59 | 5605 |
| 78 and 28 | 1092 |