Least Common Multiple (LCM) of 137 and 144
The least common multiple (LCM) of 137 and 144 is 19728.
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 137 and 144?
First, calculate the GCD of 137 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 144 = 0 remainder 137 |
| 2 | 144 ÷ 137 = 1 remainder 7 |
| 3 | 137 ÷ 7 = 19 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 52 | 5148 |
| 91 and 135 | 12285 |
| 95 and 12 | 1140 |
| 153 and 149 | 22797 |
| 121 and 49 | 5929 |