Least Common Multiple (LCM) of 57 and 36
The least common multiple (LCM) of 57 and 36 is 684.
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 36?
First, calculate the GCD of 57 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 36 = 1 remainder 21 |
| 2 | 36 ÷ 21 = 1 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 183 | 15189 |
| 66 and 125 | 8250 |
| 96 and 111 | 3552 |
| 163 and 91 | 14833 |
| 155 and 171 | 26505 |