Least Common Multiple (LCM) of 40 and 179
The least common multiple (LCM) of 40 and 179 is 7160.
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 179?
First, calculate the GCD of 40 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 179 = 0 remainder 40 |
| 2 | 179 ÷ 40 = 4 remainder 19 |
| 3 | 40 ÷ 19 = 2 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 30 | 4290 |
| 172 and 154 | 13244 |
| 96 and 98 | 4704 |
| 60 and 189 | 3780 |
| 178 and 190 | 16910 |