Least Common Multiple (LCM) of 98 and 174
The least common multiple (LCM) of 98 and 174 is 8526.
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 98 and 174?
First, calculate the GCD of 98 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 174 = 0 remainder 98 |
| 2 | 174 ÷ 98 = 1 remainder 76 |
| 3 | 98 ÷ 76 = 1 remainder 22 |
| 4 | 76 ÷ 22 = 3 remainder 10 |
| 5 | 22 ÷ 10 = 2 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 76 | 1292 |
| 33 and 23 | 759 |
| 13 and 105 | 1365 |
| 178 and 10 | 890 |
| 152 and 158 | 12008 |