Least Common Multiple (LCM) of 13 and 154
The least common multiple (LCM) of 13 and 154 is 2002.
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 154?
First, calculate the GCD of 13 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 154 = 0 remainder 13 |
| 2 | 154 ÷ 13 = 11 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 |
|---|---|
| 137 and 47 | 6439 |
| 159 and 12 | 636 |
| 74 and 171 | 12654 |
| 118 and 119 | 14042 |
| 184 and 56 | 1288 |