Least Common Multiple (LCM) of 53 and 123
The least common multiple (LCM) of 53 and 123 is 6519.
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 53 and 123?
First, calculate the GCD of 53 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 123 = 0 remainder 53 |
| 2 | 123 ÷ 53 = 2 remainder 17 |
| 3 | 53 ÷ 17 = 3 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 120 | 120 |
| 51 and 162 | 2754 |
| 199 and 114 | 22686 |
| 29 and 32 | 928 |
| 45 and 95 | 855 |