Least Common Multiple (LCM) of 108 and 14
The least common multiple (LCM) of 108 and 14 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 108 and 14?
First, calculate the GCD of 108 and 14 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 14 = 7 remainder 10 |
| 2 | 14 ÷ 10 = 1 remainder 4 |
| 3 | 10 ÷ 4 = 2 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 46 | 4600 |
| 136 and 89 | 12104 |
| 101 and 129 | 13029 |
| 127 and 67 | 8509 |
| 31 and 10 | 310 |