Least Common Multiple (LCM) of 144 and 176
The least common multiple (LCM) of 144 and 176 is 1584.
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 176?
First, calculate the GCD of 144 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 176 = 0 remainder 144 |
| 2 | 176 ÷ 144 = 1 remainder 32 |
| 3 | 144 ÷ 32 = 4 remainder 16 |
| 4 | 32 ÷ 16 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 138 | 2484 |
| 10 and 198 | 990 |
| 76 and 96 | 1824 |
| 103 and 134 | 13802 |
| 45 and 194 | 8730 |