Least Common Multiple (LCM) of 48 and 121
The least common multiple (LCM) of 48 and 121 is 5808.
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 121?
First, calculate the GCD of 48 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 121 = 0 remainder 48 |
| 2 | 121 ÷ 48 = 2 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 |
|---|---|
| 107 and 53 | 5671 |
| 110 and 90 | 990 |
| 17 and 147 | 2499 |
| 54 and 70 | 1890 |
| 128 and 155 | 19840 |