Least Common Multiple (LCM) of 65 and 49
The least common multiple (LCM) of 65 and 49 is 3185.
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 49?
First, calculate the GCD of 65 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 49 = 1 remainder 16 |
| 2 | 49 ÷ 16 = 3 remainder 1 |
| 3 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 161 | 30912 |
| 47 and 88 | 4136 |
| 115 and 170 | 3910 |
| 114 and 137 | 15618 |
| 179 and 31 | 5549 |