Least Common Multiple (LCM) of 65 and 99
The least common multiple (LCM) of 65 and 99 is 6435.
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 99?
First, calculate the GCD of 65 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 99 = 0 remainder 65 |
| 2 | 99 ÷ 65 = 1 remainder 34 |
| 3 | 65 ÷ 34 = 1 remainder 31 |
| 4 | 34 ÷ 31 = 1 remainder 3 |
| 5 | 31 ÷ 3 = 10 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 56 | 56 |
| 154 and 16 | 1232 |
| 71 and 174 | 12354 |
| 144 and 126 | 1008 |
| 114 and 30 | 570 |