Least Common Multiple (LCM) of 13 and 155
The least common multiple (LCM) of 13 and 155 is 2015.
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 155?
First, calculate the GCD of 13 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 155 = 0 remainder 13 |
| 2 | 155 ÷ 13 = 11 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 194 | 13968 |
| 60 and 105 | 420 |
| 33 and 111 | 1221 |
| 125 and 69 | 8625 |
| 54 and 36 | 108 |