Least Common Multiple (LCM) of 48 and 123
The least common multiple (LCM) of 48 and 123 is 1968.
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 123?
First, calculate the GCD of 48 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 123 = 0 remainder 48 |
| 2 | 123 ÷ 48 = 2 remainder 27 |
| 3 | 48 ÷ 27 = 1 remainder 21 |
| 4 | 27 ÷ 21 = 1 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 74 | 5846 |
| 195 and 141 | 9165 |
| 142 and 172 | 12212 |
| 154 and 94 | 7238 |
| 114 and 198 | 3762 |