Least Common Multiple (LCM) of 100 and 180
The least common multiple (LCM) of 100 and 180 is 900.
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 100 and 180?
First, calculate the GCD of 100 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 180 = 0 remainder 100 |
| 2 | 180 ÷ 100 = 1 remainder 80 |
| 3 | 100 ÷ 80 = 1 remainder 20 |
| 4 | 80 ÷ 20 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 105 | 2310 |
| 34 and 26 | 442 |
| 197 and 160 | 31520 |
| 79 and 77 | 6083 |
| 39 and 180 | 2340 |