Least Common Multiple (LCM) of 105 and 98
The least common multiple (LCM) of 105 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 105 and 98?
First, calculate the GCD of 105 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 98 = 1 remainder 7 |
| 2 | 98 ÷ 7 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 175 | 2100 |
| 122 and 82 | 5002 |
| 76 and 66 | 2508 |
| 113 and 15 | 1695 |
| 33 and 65 | 2145 |