Least Common Multiple (LCM) of 144 and 190
The least common multiple (LCM) of 144 and 190 is 13680.
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 190?
First, calculate the GCD of 144 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 190 = 0 remainder 144 |
| 2 | 190 ÷ 144 = 1 remainder 46 |
| 3 | 144 ÷ 46 = 3 remainder 6 |
| 4 | 46 ÷ 6 = 7 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 23 | 1702 |
| 63 and 31 | 1953 |
| 198 and 160 | 15840 |
| 56 and 109 | 6104 |
| 109 and 99 | 10791 |