Least Common Multiple (LCM) of 101 and 144
The least common multiple (LCM) of 101 and 144 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 101 and 144?
First, calculate the GCD of 101 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 144 = 0 remainder 101 |
| 2 | 144 ÷ 101 = 1 remainder 43 |
| 3 | 101 ÷ 43 = 2 remainder 15 |
| 4 | 43 ÷ 15 = 2 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 183 | 34770 |
| 124 and 125 | 15500 |
| 110 and 138 | 7590 |
| 163 and 176 | 28688 |
| 50 and 83 | 4150 |