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 |
|---|---|
| 149 and 117 | 17433 |
| 186 and 38 | 3534 |
| 188 and 145 | 27260 |
| 138 and 36 | 828 |
| 167 and 116 | 19372 |