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 |
|---|---|
| 91 and 90 | 8190 |
| 115 and 38 | 4370 |
| 13 and 46 | 598 |
| 174 and 94 | 8178 |
| 30 and 185 | 1110 |