Least Common Multiple (LCM) of 48 and 144
The least common multiple (LCM) of 48 and 144 is 144.
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 48 and 144?
First, calculate the GCD of 48 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 144 = 0 remainder 48 |
| 2 | 144 ÷ 48 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 75 | 1350 |
| 175 and 169 | 29575 |
| 142 and 188 | 13348 |
| 139 and 172 | 23908 |
| 114 and 125 | 14250 |