Least Common Multiple (LCM) of 17 and 61
The least common multiple (LCM) of 17 and 61 is 1037.
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 61?
First, calculate the GCD of 17 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 61 = 0 remainder 17 |
| 2 | 61 ÷ 17 = 3 remainder 10 |
| 3 | 17 ÷ 10 = 1 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 102 | 5916 |
| 125 and 101 | 12625 |
| 100 and 59 | 5900 |
| 27 and 134 | 3618 |
| 45 and 200 | 1800 |