Least Common Multiple (LCM) of 65 and 144
The least common multiple (LCM) of 65 and 144 is 9360.
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 144?
First, calculate the GCD of 65 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 144 = 0 remainder 65 |
| 2 | 144 ÷ 65 = 2 remainder 14 |
| 3 | 65 ÷ 14 = 4 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 85 | 10030 |
| 111 and 16 | 1776 |
| 54 and 67 | 3618 |
| 188 and 23 | 4324 |
| 101 and 50 | 5050 |