Least Common Multiple (LCM) of 123 and 48
The least common multiple (LCM) of 123 and 48 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 123 and 48?
First, calculate the GCD of 123 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 48 = 2 remainder 27 |
| 2 | 48 ÷ 27 = 1 remainder 21 |
| 3 | 27 ÷ 21 = 1 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 17 | 2618 |
| 106 and 191 | 20246 |
| 143 and 78 | 858 |
| 156 and 36 | 468 |
| 170 and 74 | 6290 |