Least Common Multiple (LCM) of 13 and 109
The least common multiple (LCM) of 13 and 109 is 1417.
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 109?
First, calculate the GCD of 13 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 109 = 0 remainder 13 |
| 2 | 109 ÷ 13 = 8 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 141 | 14100 |
| 11 and 81 | 891 |
| 115 and 128 | 14720 |
| 141 and 38 | 5358 |
| 157 and 86 | 13502 |