Least Common Multiple (LCM) of 30 and 200
The least common multiple (LCM) of 30 and 200 is 600.
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 30 and 200?
First, calculate the GCD of 30 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 200 = 0 remainder 30 |
| 2 | 200 ÷ 30 = 6 remainder 20 |
| 3 | 30 ÷ 20 = 1 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 36 | 7164 |
| 132 and 80 | 2640 |
| 153 and 196 | 29988 |
| 176 and 10 | 880 |
| 14 and 155 | 2170 |