Least Common Multiple (LCM) of 42 and 65
The least common multiple (LCM) of 42 and 65 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 42 and 65?
First, calculate the GCD of 42 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 65 = 0 remainder 42 |
| 2 | 65 ÷ 42 = 1 remainder 23 |
| 3 | 42 ÷ 23 = 1 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 |
|---|---|
| 38 and 193 | 7334 |
| 132 and 25 | 3300 |
| 147 and 189 | 1323 |
| 135 and 156 | 7020 |
| 98 and 17 | 1666 |