Least Common Multiple (LCM) of 13 and 101
The least common multiple (LCM) of 13 and 101 is 1313.
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 101?
First, calculate the GCD of 13 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 101 = 0 remainder 13 |
| 2 | 101 ÷ 13 = 7 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 |
|---|---|
| 183 and 160 | 29280 |
| 22 and 113 | 2486 |
| 42 and 19 | 798 |
| 135 and 117 | 1755 |
| 16 and 198 | 1584 |