Least Common Multiple (LCM) of 57 and 147
The least common multiple (LCM) of 57 and 147 is 2793.
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 147?
First, calculate the GCD of 57 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 147 = 0 remainder 57 |
| 2 | 147 ÷ 57 = 2 remainder 33 |
| 3 | 57 ÷ 33 = 1 remainder 24 |
| 4 | 33 ÷ 24 = 1 remainder 9 |
| 5 | 24 ÷ 9 = 2 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 13 | 1456 |
| 115 and 112 | 12880 |
| 128 and 153 | 19584 |
| 198 and 159 | 10494 |
| 40 and 17 | 680 |