Least Common Multiple (LCM) of 65 and 110
The least common multiple (LCM) of 65 and 110 is 1430.
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 110?
First, calculate the GCD of 65 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 110 = 0 remainder 65 |
| 2 | 110 ÷ 65 = 1 remainder 45 |
| 3 | 65 ÷ 45 = 1 remainder 20 |
| 4 | 45 ÷ 20 = 2 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 137 | 24660 |
| 69 and 18 | 414 |
| 38 and 47 | 1786 |
| 158 and 165 | 26070 |
| 115 and 145 | 3335 |