Least Common Multiple (LCM) of 57 and 165
The least common multiple (LCM) of 57 and 165 is 3135.
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 165?
First, calculate the GCD of 57 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 165 = 0 remainder 57 |
| 2 | 165 ÷ 57 = 2 remainder 51 |
| 3 | 57 ÷ 51 = 1 remainder 6 |
| 4 | 51 ÷ 6 = 8 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 127 | 13716 |
| 116 and 98 | 5684 |
| 153 and 100 | 15300 |
| 61 and 174 | 10614 |
| 95 and 136 | 12920 |