Least Common Multiple (LCM) of 149 and 65
The least common multiple (LCM) of 149 and 65 is 9685.
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 149 and 65?
First, calculate the GCD of 149 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 65 = 2 remainder 19 |
| 2 | 65 ÷ 19 = 3 remainder 8 |
| 3 | 19 ÷ 8 = 2 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 45 | 4365 |
| 17 and 126 | 2142 |
| 196 and 14 | 196 |
| 136 and 82 | 5576 |
| 146 and 54 | 3942 |