Least Common Multiple (LCM) of 98 and 158
The least common multiple (LCM) of 98 and 158 is 7742.
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 158?
First, calculate the GCD of 98 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 158 = 0 remainder 98 |
| 2 | 158 ÷ 98 = 1 remainder 60 |
| 3 | 98 ÷ 60 = 1 remainder 38 |
| 4 | 60 ÷ 38 = 1 remainder 22 |
| 5 | 38 ÷ 22 = 1 remainder 16 |
| 6 | 22 ÷ 16 = 1 remainder 6 |
| 7 | 16 ÷ 6 = 2 remainder 4 |
| 8 | 6 ÷ 4 = 1 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 188 | 18612 |
| 36 and 80 | 720 |
| 145 and 81 | 11745 |
| 105 and 107 | 11235 |
| 116 and 35 | 4060 |