Least Common Multiple (LCM) of 17 and 72
The least common multiple (LCM) of 17 and 72 is 1224.
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 17 and 72?
First, calculate the GCD of 17 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 72 = 0 remainder 17 |
| 2 | 72 ÷ 17 = 4 remainder 4 |
| 3 | 17 ÷ 4 = 4 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 126 | 1260 |
| 14 and 177 | 2478 |
| 199 and 173 | 34427 |
| 96 and 155 | 14880 |
| 179 and 194 | 34726 |