Least Common Multiple (LCM) of 57 and 92
The least common multiple (LCM) of 57 and 92 is 5244.
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 92?
First, calculate the GCD of 57 and 92 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 92 = 0 remainder 57 |
| 2 | 92 ÷ 57 = 1 remainder 35 |
| 3 | 57 ÷ 35 = 1 remainder 22 |
| 4 | 35 ÷ 22 = 1 remainder 13 |
| 5 | 22 ÷ 13 = 1 remainder 9 |
| 6 | 13 ÷ 9 = 1 remainder 4 |
| 7 | 9 ÷ 4 = 2 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 169 | 18928 |
| 198 and 157 | 31086 |
| 105 and 91 | 1365 |
| 132 and 50 | 3300 |
| 120 and 131 | 15720 |