Least Common Multiple (LCM) of 65 and 42
The least common multiple (LCM) of 65 and 42 is 2730.
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 42?
First, calculate the GCD of 65 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 42 = 1 remainder 23 |
| 2 | 42 ÷ 23 = 1 remainder 19 |
| 3 | 23 ÷ 19 = 1 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 81 | 9882 |
| 185 and 156 | 28860 |
| 140 and 163 | 22820 |
| 55 and 30 | 330 |
| 26 and 61 | 1586 |