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 |
|---|---|
| 43 and 80 | 3440 |
| 110 and 70 | 770 |
| 96 and 48 | 96 |
| 112 and 117 | 13104 |
| 135 and 91 | 12285 |