Least Common Multiple (LCM) of 57 and 110
The least common multiple (LCM) of 57 and 110 is 6270.
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 110?
First, calculate the GCD of 57 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 110 = 0 remainder 57 |
| 2 | 110 ÷ 57 = 1 remainder 53 |
| 3 | 57 ÷ 53 = 1 remainder 4 |
| 4 | 53 ÷ 4 = 13 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 73 | 11023 |
| 158 and 160 | 12640 |
| 144 and 35 | 5040 |
| 192 and 196 | 9408 |
| 30 and 122 | 1830 |