Least Common Multiple (LCM) of 113 and 144
The least common multiple (LCM) of 113 and 144 is 16272.
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 113 and 144?
First, calculate the GCD of 113 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 144 = 0 remainder 113 |
| 2 | 144 ÷ 113 = 1 remainder 31 |
| 3 | 113 ÷ 31 = 3 remainder 20 |
| 4 | 31 ÷ 20 = 1 remainder 11 |
| 5 | 20 ÷ 11 = 1 remainder 9 |
| 6 | 11 ÷ 9 = 1 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 76 | 5700 |
| 125 and 148 | 18500 |
| 187 and 107 | 20009 |
| 144 and 106 | 7632 |
| 166 and 109 | 18094 |