Least Common Multiple (LCM) of 17 and 46
The least common multiple (LCM) of 17 and 46 is 782.
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 46?
First, calculate the GCD of 17 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 46 = 0 remainder 17 |
| 2 | 46 ÷ 17 = 2 remainder 12 |
| 3 | 17 ÷ 12 = 1 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 56 | 10920 |
| 76 and 37 | 2812 |
| 60 and 165 | 660 |
| 151 and 90 | 13590 |
| 39 and 142 | 5538 |