Least Common Multiple (LCM) of 17 and 60
The least common multiple (LCM) of 17 and 60 is 1020.
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 60?
First, calculate the GCD of 17 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 60 = 0 remainder 17 |
| 2 | 60 ÷ 17 = 3 remainder 9 |
| 3 | 17 ÷ 9 = 1 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 79 | 14615 |
| 24 and 15 | 120 |
| 186 and 40 | 3720 |
| 83 and 116 | 9628 |
| 146 and 118 | 8614 |