Least Common Multiple (LCM) of 144 and 49
The least common multiple (LCM) of 144 and 49 is 7056.
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 49?
First, calculate the GCD of 144 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 49 = 2 remainder 46 |
| 2 | 49 ÷ 46 = 1 remainder 3 |
| 3 | 46 ÷ 3 = 15 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 173 | 17127 |
| 180 and 89 | 16020 |
| 193 and 24 | 4632 |
| 141 and 170 | 23970 |
| 182 and 179 | 32578 |