Least Common Multiple (LCM) of 48 and 73
The least common multiple (LCM) of 48 and 73 is 3504.
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 73?
First, calculate the GCD of 48 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 73 = 0 remainder 48 |
| 2 | 73 ÷ 48 = 1 remainder 25 |
| 3 | 48 ÷ 25 = 1 remainder 23 |
| 4 | 25 ÷ 23 = 1 remainder 2 |
| 5 | 23 ÷ 2 = 11 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 181 | 23892 |
| 180 and 169 | 30420 |
| 103 and 112 | 11536 |
| 138 and 57 | 2622 |
| 173 and 24 | 4152 |