Least Common Multiple (LCM) of 61 and 98
The least common multiple (LCM) of 61 and 98 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 61 and 98?
First, calculate the GCD of 61 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 98 = 0 remainder 61 |
| 2 | 98 ÷ 61 = 1 remainder 37 |
| 3 | 61 ÷ 37 = 1 remainder 24 |
| 4 | 37 ÷ 24 = 1 remainder 13 |
| 5 | 24 ÷ 13 = 1 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 51 | 2805 |
| 183 and 169 | 30927 |
| 67 and 168 | 11256 |
| 157 and 123 | 19311 |
| 15 and 47 | 705 |