Least Common Multiple (LCM) of 48 and 122
The least common multiple (LCM) of 48 and 122 is 2928.
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 122?
First, calculate the GCD of 48 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 122 = 0 remainder 48 |
| 2 | 122 ÷ 48 = 2 remainder 26 |
| 3 | 48 ÷ 26 = 1 remainder 22 |
| 4 | 26 ÷ 22 = 1 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 90 | 720 |
| 196 and 199 | 39004 |
| 53 and 19 | 1007 |
| 199 and 55 | 10945 |
| 194 and 11 | 2134 |