Least Common Multiple (LCM) of 68 and 98
The least common multiple (LCM) of 68 and 98 is 3332.
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 68 and 98?
First, calculate the GCD of 68 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 98 = 0 remainder 68 |
| 2 | 98 ÷ 68 = 1 remainder 30 |
| 3 | 68 ÷ 30 = 2 remainder 8 |
| 4 | 30 ÷ 8 = 3 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 44 | 440 |
| 68 and 65 | 4420 |
| 50 and 60 | 300 |
| 32 and 54 | 864 |
| 177 and 124 | 21948 |