Least Common Multiple (LCM) of 100 and 30
The least common multiple (LCM) of 100 and 30 is 300.
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 30?
First, calculate the GCD of 100 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 30 = 3 remainder 10 |
| 2 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 10 | 810 |
| 32 and 55 | 1760 |
| 195 and 26 | 390 |
| 103 and 21 | 2163 |
| 171 and 124 | 21204 |