Least Common Multiple (LCM) of 13 and 50
The least common multiple (LCM) of 13 and 50 is 650.
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 13 and 50?
First, calculate the GCD of 13 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 50 = 0 remainder 13 |
| 2 | 50 ÷ 13 = 3 remainder 11 |
| 3 | 13 ÷ 11 = 1 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 143 | 14729 |
| 171 and 108 | 2052 |
| 107 and 73 | 7811 |
| 101 and 64 | 6464 |
| 152 and 158 | 12008 |