Least Common Multiple (LCM) of 13 and 102
The least common multiple (LCM) of 13 and 102 is 1326.
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 102?
First, calculate the GCD of 13 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 102 = 0 remainder 13 |
| 2 | 102 ÷ 13 = 7 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 |
|---|---|
| 126 and 169 | 21294 |
| 180 and 133 | 23940 |
| 186 and 42 | 1302 |
| 175 and 22 | 3850 |
| 145 and 31 | 4495 |