Least Common Multiple (LCM) of 180 and 43
The least common multiple (LCM) of 180 and 43 is 7740.
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 180 and 43?
First, calculate the GCD of 180 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 43 = 4 remainder 8 |
| 2 | 43 ÷ 8 = 5 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 22 | 506 |
| 96 and 112 | 672 |
| 13 and 178 | 2314 |
| 106 and 169 | 17914 |
| 35 and 62 | 2170 |