Least Common Multiple (LCM) of 144 and 101
The least common multiple (LCM) of 144 and 101 is 14544.
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 101?
First, calculate the GCD of 144 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 101 = 1 remainder 43 |
| 2 | 101 ÷ 43 = 2 remainder 15 |
| 3 | 43 ÷ 15 = 2 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 80 | 6960 |
| 126 and 167 | 21042 |
| 164 and 65 | 10660 |
| 53 and 109 | 5777 |
| 178 and 144 | 12816 |