Least Common Multiple (LCM) of 169 and 144
The least common multiple (LCM) of 169 and 144 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 169 and 144?
First, calculate the GCD of 169 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 144 = 1 remainder 25 |
| 2 | 144 ÷ 25 = 5 remainder 19 |
| 3 | 25 ÷ 19 = 1 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 39 | 4290 |
| 165 and 173 | 28545 |
| 20 and 129 | 2580 |
| 38 and 95 | 190 |
| 189 and 152 | 28728 |