Least Common Multiple (LCM) of 52 and 123
The least common multiple (LCM) of 52 and 123 is 6396.
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 52 and 123?
First, calculate the GCD of 52 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 123 = 0 remainder 52 |
| 2 | 123 ÷ 52 = 2 remainder 19 |
| 3 | 52 ÷ 19 = 2 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 148 | 24124 |
| 191 and 175 | 33425 |
| 78 and 47 | 3666 |
| 62 and 200 | 6200 |
| 164 and 114 | 9348 |