Least Common Multiple (LCM) of 10 and 30
The least common multiple (LCM) of 10 and 30 is 30.
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 10 and 30?
First, calculate the GCD of 10 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 30 = 0 remainder 10 |
| 2 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 189 | 2457 |
| 123 and 29 | 3567 |
| 129 and 18 | 774 |
| 140 and 150 | 2100 |
| 192 and 194 | 18624 |