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 |
|---|---|
| 120 and 111 | 4440 |
| 192 and 108 | 1728 |
| 124 and 30 | 1860 |
| 31 and 189 | 5859 |
| 189 and 125 | 23625 |