Least Common Multiple (LCM) of 53 and 103
The least common multiple (LCM) of 53 and 103 is 5459.
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 103?
First, calculate the GCD of 53 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 103 = 0 remainder 53 |
| 2 | 103 ÷ 53 = 1 remainder 50 |
| 3 | 53 ÷ 50 = 1 remainder 3 |
| 4 | 50 ÷ 3 = 16 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 48 | 1392 |
| 21 and 91 | 273 |
| 36 and 87 | 1044 |
| 113 and 115 | 12995 |
| 87 and 92 | 8004 |