Least Common Multiple (LCM) of 98 and 154
The least common multiple (LCM) of 98 and 154 is 1078.
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 154?
First, calculate the GCD of 98 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 154 = 0 remainder 98 |
| 2 | 154 ÷ 98 = 1 remainder 56 |
| 3 | 98 ÷ 56 = 1 remainder 42 |
| 4 | 56 ÷ 42 = 1 remainder 14 |
| 5 | 42 ÷ 14 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 102 | 510 |
| 130 and 96 | 6240 |
| 114 and 126 | 2394 |
| 30 and 173 | 5190 |
| 32 and 125 | 4000 |