Least Common Multiple (LCM) of 98 and 61
The least common multiple (LCM) of 98 and 61 is 5978.
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 61?
First, calculate the GCD of 98 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 61 = 1 remainder 37 |
| 2 | 61 ÷ 37 = 1 remainder 24 |
| 3 | 37 ÷ 24 = 1 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 14 | 1694 |
| 104 and 131 | 13624 |
| 113 and 120 | 13560 |
| 129 and 70 | 9030 |
| 196 and 54 | 5292 |