Least Common Multiple (LCM) of 13 and 51
The least common multiple (LCM) of 13 and 51 is 663.
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 51?
First, calculate the GCD of 13 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 51 = 0 remainder 13 |
| 2 | 51 ÷ 13 = 3 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 149 | 15347 |
| 24 and 18 | 72 |
| 164 and 152 | 6232 |
| 49 and 55 | 2695 |
| 51 and 112 | 5712 |