Least Common Multiple (LCM) of 180 and 196
The least common multiple (LCM) of 180 and 196 is 8820.
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 196?
First, calculate the GCD of 180 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 196 = 0 remainder 180 |
| 2 | 196 ÷ 180 = 1 remainder 16 |
| 3 | 180 ÷ 16 = 11 remainder 4 |
| 4 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 162 | 2754 |
| 103 and 36 | 3708 |
| 176 and 182 | 16016 |
| 59 and 179 | 10561 |
| 81 and 72 | 648 |