Least Common Multiple (LCM) of 71 and 98
The least common multiple (LCM) of 71 and 98 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 71 and 98?
First, calculate the GCD of 71 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 98 = 0 remainder 71 |
| 2 | 98 ÷ 71 = 1 remainder 27 |
| 3 | 71 ÷ 27 = 2 remainder 17 |
| 4 | 27 ÷ 17 = 1 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 16 | 368 |
| 120 and 87 | 3480 |
| 135 and 29 | 3915 |
| 171 and 130 | 22230 |
| 95 and 159 | 15105 |