Least Common Multiple (LCM) of 65 and 24
The least common multiple (LCM) of 65 and 24 is 1560.
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 24?
First, calculate the GCD of 65 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 24 = 2 remainder 17 |
| 2 | 24 ÷ 17 = 1 remainder 7 |
| 3 | 17 ÷ 7 = 2 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 110 | 4730 |
| 195 and 139 | 27105 |
| 184 and 108 | 4968 |
| 172 and 47 | 8084 |
| 61 and 200 | 12200 |