Least Common Multiple (LCM) of 14 and 149
The least common multiple (LCM) of 14 and 149 is 2086.
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 149?
First, calculate the GCD of 14 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 149 = 0 remainder 14 |
| 2 | 149 ÷ 14 = 10 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 85 | 7735 |
| 153 and 197 | 30141 |
| 51 and 106 | 5406 |
| 32 and 145 | 4640 |
| 15 and 95 | 285 |