Least Common Multiple (LCM) of 48 and 78
The least common multiple (LCM) of 48 and 78 is 624.
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 78?
First, calculate the GCD of 48 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 78 = 0 remainder 48 |
| 2 | 78 ÷ 48 = 1 remainder 30 |
| 3 | 48 ÷ 30 = 1 remainder 18 |
| 4 | 30 ÷ 18 = 1 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 36 | 3420 |
| 13 and 11 | 143 |
| 119 and 200 | 23800 |
| 13 and 20 | 260 |
| 200 and 75 | 600 |