Least Common Multiple (LCM) of 45 and 57
The least common multiple (LCM) of 45 and 57 is 855.
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 45 and 57?
First, calculate the GCD of 45 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 57 = 0 remainder 45 |
| 2 | 57 ÷ 45 = 1 remainder 12 |
| 3 | 45 ÷ 12 = 3 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 193 | 27599 |
| 55 and 165 | 165 |
| 103 and 112 | 11536 |
| 63 and 198 | 1386 |
| 173 and 133 | 23009 |