Least Common Multiple (LCM) of 13 and 72
The least common multiple (LCM) of 13 and 72 is 936.
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 72?
First, calculate the GCD of 13 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 72 = 0 remainder 13 |
| 2 | 72 ÷ 13 = 5 remainder 7 |
| 3 | 13 ÷ 7 = 1 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 63 | 5607 |
| 189 and 73 | 13797 |
| 190 and 161 | 30590 |
| 104 and 123 | 12792 |
| 138 and 126 | 2898 |