Least Common Multiple (LCM) of 144 and 85
The least common multiple (LCM) of 144 and 85 is 12240.
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 144 and 85?
First, calculate the GCD of 144 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 85 = 1 remainder 59 |
| 2 | 85 ÷ 59 = 1 remainder 26 |
| 3 | 59 ÷ 26 = 2 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 77 | 2926 |
| 115 and 61 | 7015 |
| 178 and 123 | 21894 |
| 134 and 44 | 2948 |
| 75 and 200 | 600 |