Least Common Multiple (LCM) of 120 and 65
The least common multiple (LCM) of 120 and 65 is 1560.
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 120 and 65?
First, calculate the GCD of 120 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 65 = 1 remainder 55 |
| 2 | 65 ÷ 55 = 1 remainder 10 |
| 3 | 55 ÷ 10 = 5 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 199 | 25472 |
| 40 and 38 | 760 |
| 84 and 26 | 1092 |
| 199 and 197 | 39203 |
| 92 and 105 | 9660 |