Least Common Multiple (LCM) of 144 and 191
The least common multiple (LCM) of 144 and 191 is 27504.
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 191?
First, calculate the GCD of 144 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 191 = 0 remainder 144 |
| 2 | 191 ÷ 144 = 1 remainder 47 |
| 3 | 144 ÷ 47 = 3 remainder 3 |
| 4 | 47 ÷ 3 = 15 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 63 | 1071 |
| 164 and 190 | 15580 |
| 20 and 22 | 220 |
| 113 and 64 | 7232 |
| 73 and 110 | 8030 |