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 |
|---|---|
| 137 and 20 | 2740 |
| 23 and 153 | 3519 |
| 141 and 128 | 18048 |
| 87 and 152 | 13224 |
| 147 and 130 | 19110 |