Least Common Multiple (LCM) of 46 and 17
The least common multiple (LCM) of 46 and 17 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 46 and 17?
First, calculate the GCD of 46 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 17 = 2 remainder 12 |
| 2 | 17 ÷ 12 = 1 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 119 | 12376 |
| 179 and 62 | 11098 |
| 186 and 132 | 4092 |
| 39 and 181 | 7059 |
| 155 and 126 | 19530 |