Least Common Multiple (LCM) of 144 and 194
The least common multiple (LCM) of 144 and 194 is 13968.
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 194?
First, calculate the GCD of 144 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 194 = 0 remainder 144 |
| 2 | 194 ÷ 144 = 1 remainder 50 |
| 3 | 144 ÷ 50 = 2 remainder 44 |
| 4 | 50 ÷ 44 = 1 remainder 6 |
| 5 | 44 ÷ 6 = 7 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 30 | 3630 |
| 31 and 152 | 4712 |
| 38 and 106 | 2014 |
| 99 and 81 | 891 |
| 16 and 171 | 2736 |