Least Common Multiple (LCM) of 57 and 98
The least common multiple (LCM) of 57 and 98 is 5586.
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 57 and 98?
First, calculate the GCD of 57 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 98 = 0 remainder 57 |
| 2 | 98 ÷ 57 = 1 remainder 41 |
| 3 | 57 ÷ 41 = 1 remainder 16 |
| 4 | 41 ÷ 16 = 2 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 172 | 8084 |
| 173 and 89 | 15397 |
| 155 and 40 | 1240 |
| 122 and 165 | 20130 |
| 82 and 170 | 6970 |