Least Common Multiple (LCM) of 48 and 67
The least common multiple (LCM) of 48 and 67 is 3216.
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 67?
First, calculate the GCD of 48 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 67 = 0 remainder 48 |
| 2 | 67 ÷ 48 = 1 remainder 19 |
| 3 | 48 ÷ 19 = 2 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 48 | 720 |
| 100 and 132 | 3300 |
| 135 and 190 | 5130 |
| 40 and 156 | 1560 |
| 126 and 61 | 7686 |