Least Common Multiple (LCM) of 65 and 149
The least common multiple (LCM) of 65 and 149 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 65 and 149?
First, calculate the GCD of 65 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 149 = 0 remainder 65 |
| 2 | 149 ÷ 65 = 2 remainder 19 |
| 3 | 65 ÷ 19 = 3 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 137 | 11234 |
| 45 and 167 | 7515 |
| 25 and 11 | 275 |
| 165 and 32 | 5280 |
| 174 and 136 | 11832 |