Least Common Multiple (LCM) of 65 and 119
The least common multiple (LCM) of 65 and 119 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 65 and 119?
First, calculate the GCD of 65 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 119 = 0 remainder 65 |
| 2 | 119 ÷ 65 = 1 remainder 54 |
| 3 | 65 ÷ 54 = 1 remainder 11 |
| 4 | 54 ÷ 11 = 4 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 172 | 6708 |
| 178 and 103 | 18334 |
| 69 and 98 | 6762 |
| 109 and 103 | 11227 |
| 150 and 78 | 1950 |