Least Common Multiple (LCM) of 20 and 48
The least common multiple (LCM) of 20 and 48 is 240.
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 20 and 48?
First, calculate the GCD of 20 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 48 = 0 remainder 20 |
| 2 | 48 ÷ 20 = 2 remainder 8 |
| 3 | 20 ÷ 8 = 2 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 145 | 19285 |
| 172 and 20 | 860 |
| 110 and 153 | 16830 |
| 36 and 107 | 3852 |
| 37 and 171 | 6327 |