Least Common Multiple (LCM) of 98 and 71
The least common multiple (LCM) of 98 and 71 is 6958.
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 71?
First, calculate the GCD of 98 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 71 = 1 remainder 27 |
| 2 | 71 ÷ 27 = 2 remainder 17 |
| 3 | 27 ÷ 17 = 1 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 89 | 17622 |
| 171 and 74 | 12654 |
| 135 and 115 | 3105 |
| 129 and 138 | 5934 |
| 110 and 146 | 8030 |