Least Common Multiple (LCM) of 123 and 52
The least common multiple (LCM) of 123 and 52 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 123 and 52?
First, calculate the GCD of 123 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 52 = 2 remainder 19 |
| 2 | 52 ÷ 19 = 2 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 10 | 370 |
| 116 and 46 | 2668 |
| 32 and 127 | 4064 |
| 136 and 113 | 15368 |
| 195 and 167 | 32565 |