Least Common Multiple (LCM) of 67 and 98
The least common multiple (LCM) of 67 and 98 is 6566.
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 67 and 98?
First, calculate the GCD of 67 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 98 = 0 remainder 67 |
| 2 | 98 ÷ 67 = 1 remainder 31 |
| 3 | 67 ÷ 31 = 2 remainder 5 |
| 4 | 31 ÷ 5 = 6 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 49 | 7301 |
| 81 and 179 | 14499 |
| 105 and 182 | 2730 |
| 58 and 71 | 4118 |
| 70 and 173 | 12110 |