Least Common Multiple (LCM) of 78 and 48
The least common multiple (LCM) of 78 and 48 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 78 and 48?
First, calculate the GCD of 78 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 48 = 1 remainder 30 |
| 2 | 48 ÷ 30 = 1 remainder 18 |
| 3 | 30 ÷ 18 = 1 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 48 | 1968 |
| 167 and 198 | 33066 |
| 130 and 82 | 5330 |
| 104 and 158 | 8216 |
| 111 and 157 | 17427 |