Least Common Multiple (LCM) of 48 and 59
The least common multiple (LCM) of 48 and 59 is 2832.
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 59?
First, calculate the GCD of 48 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 59 = 0 remainder 48 |
| 2 | 59 ÷ 48 = 1 remainder 11 |
| 3 | 48 ÷ 11 = 4 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 100 | 200 |
| 27 and 61 | 1647 |
| 65 and 106 | 6890 |
| 129 and 111 | 4773 |
| 132 and 60 | 660 |