Least Common Multiple (LCM) of 30 and 98
The least common multiple (LCM) of 30 and 98 is 1470.
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 98?
First, calculate the GCD of 30 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 98 = 0 remainder 30 |
| 2 | 98 ÷ 30 = 3 remainder 8 |
| 3 | 30 ÷ 8 = 3 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 126 | 1134 |
| 27 and 45 | 135 |
| 123 and 125 | 15375 |
| 83 and 199 | 16517 |
| 65 and 144 | 9360 |