Least Common Multiple (LCM) of 40 and 17
The least common multiple (LCM) of 40 and 17 is 680.
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 40 and 17?
First, calculate the GCD of 40 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 17 = 2 remainder 6 |
| 2 | 17 ÷ 6 = 2 remainder 5 |
| 3 | 6 ÷ 5 = 1 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 187 | 5236 |
| 146 and 145 | 21170 |
| 155 and 154 | 23870 |
| 180 and 16 | 720 |
| 69 and 99 | 2277 |