Least Common Multiple (LCM) of 31 and 98
The least common multiple (LCM) of 31 and 98 is 3038.
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 31 and 98?
First, calculate the GCD of 31 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 98 = 0 remainder 31 |
| 2 | 98 ÷ 31 = 3 remainder 5 |
| 3 | 31 ÷ 5 = 6 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 101 | 5050 |
| 39 and 45 | 585 |
| 11 and 110 | 110 |
| 188 and 184 | 8648 |
| 95 and 96 | 9120 |