Least Common Multiple (LCM) of 24 and 85
The least common multiple (LCM) of 24 and 85 is 2040.
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 24 and 85?
First, calculate the GCD of 24 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 85 = 0 remainder 24 |
| 2 | 85 ÷ 24 = 3 remainder 13 |
| 3 | 24 ÷ 13 = 1 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 129 | 1032 |
| 120 and 191 | 22920 |
| 130 and 30 | 390 |
| 111 and 64 | 7104 |
| 182 and 80 | 7280 |