Least Common Multiple (LCM) of 165 and 56
The least common multiple (LCM) of 165 and 56 is 9240.
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 165 and 56?
First, calculate the GCD of 165 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 56 = 2 remainder 53 |
| 2 | 56 ÷ 53 = 1 remainder 3 |
| 3 | 53 ÷ 3 = 17 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 22 | 1474 |
| 117 and 59 | 6903 |
| 154 and 10 | 770 |
| 105 and 106 | 11130 |
| 61 and 134 | 8174 |