Least Common Multiple (LCM) of 65 and 88
The least common multiple (LCM) of 65 and 88 is 5720.
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 88?
First, calculate the GCD of 65 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 88 = 0 remainder 65 |
| 2 | 88 ÷ 65 = 1 remainder 23 |
| 3 | 65 ÷ 23 = 2 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 119 | 714 |
| 83 and 80 | 6640 |
| 17 and 96 | 1632 |
| 169 and 46 | 7774 |
| 86 and 86 | 86 |