Least Common Multiple (LCM) of 48 and 68
The least common multiple (LCM) of 48 and 68 is 816.
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 68?
First, calculate the GCD of 48 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 68 = 0 remainder 48 |
| 2 | 68 ÷ 48 = 1 remainder 20 |
| 3 | 48 ÷ 20 = 2 remainder 8 |
| 4 | 20 ÷ 8 = 2 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 98 | 1568 |
| 61 and 53 | 3233 |
| 84 and 135 | 3780 |
| 136 and 85 | 680 |
| 146 and 163 | 23798 |