Least Common Multiple (LCM) of 98 and 159
The least common multiple (LCM) of 98 and 159 is 15582.
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 159?
First, calculate the GCD of 98 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 159 = 0 remainder 98 |
| 2 | 159 ÷ 98 = 1 remainder 61 |
| 3 | 98 ÷ 61 = 1 remainder 37 |
| 4 | 61 ÷ 37 = 1 remainder 24 |
| 5 | 37 ÷ 24 = 1 remainder 13 |
| 6 | 24 ÷ 13 = 1 remainder 11 |
| 7 | 13 ÷ 11 = 1 remainder 2 |
| 8 | 11 ÷ 2 = 5 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 161 | 14329 |
| 55 and 161 | 8855 |
| 135 and 138 | 6210 |
| 53 and 90 | 4770 |
| 130 and 43 | 5590 |