Least Common Multiple (LCM) of 144 and 43
The least common multiple (LCM) of 144 and 43 is 6192.
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 43?
First, calculate the GCD of 144 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 43 = 3 remainder 15 |
| 2 | 43 ÷ 15 = 2 remainder 13 |
| 3 | 15 ÷ 13 = 1 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 21 | 1113 |
| 126 and 197 | 24822 |
| 200 and 138 | 13800 |
| 23 and 156 | 3588 |
| 156 and 134 | 10452 |