Least Common Multiple (LCM) of 119 and 65
The least common multiple (LCM) of 119 and 65 is 7735.
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 119 and 65?
First, calculate the GCD of 119 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 65 = 1 remainder 54 |
| 2 | 65 ÷ 54 = 1 remainder 11 |
| 3 | 54 ÷ 11 = 4 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 48 | 336 |
| 41 and 40 | 1640 |
| 42 and 104 | 2184 |
| 49 and 64 | 3136 |
| 106 and 180 | 9540 |