Least Common Multiple (LCM) of 144 and 169
The least common multiple (LCM) of 144 and 169 is 24336.
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 169?
First, calculate the GCD of 144 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 169 = 0 remainder 144 |
| 2 | 169 ÷ 144 = 1 remainder 25 |
| 3 | 144 ÷ 25 = 5 remainder 19 |
| 4 | 25 ÷ 19 = 1 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 45 | 3060 |
| 71 and 105 | 7455 |
| 161 and 93 | 14973 |
| 11 and 31 | 341 |
| 193 and 192 | 37056 |