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 |
|---|---|
| 115 and 52 | 5980 |
| 40 and 200 | 200 |
| 157 and 33 | 5181 |
| 122 and 165 | 20130 |
| 152 and 148 | 5624 |