Least Common Multiple (LCM) of 13 and 49
The least common multiple (LCM) of 13 and 49 is 637.
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 49?
First, calculate the GCD of 13 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 49 = 0 remainder 13 |
| 2 | 49 ÷ 13 = 3 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 42 | 1806 |
| 149 and 80 | 11920 |
| 54 and 23 | 1242 |
| 54 and 89 | 4806 |
| 81 and 31 | 2511 |