Least Common Multiple (LCM) of 65 and 142
The least common multiple (LCM) of 65 and 142 is 9230.
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 142?
First, calculate the GCD of 65 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 142 = 0 remainder 65 |
| 2 | 142 ÷ 65 = 2 remainder 12 |
| 3 | 65 ÷ 12 = 5 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 72 | 504 |
| 144 and 86 | 6192 |
| 175 and 72 | 12600 |
| 30 and 159 | 1590 |
| 89 and 32 | 2848 |