Least Common Multiple (LCM) of 112 and 165
The least common multiple (LCM) of 112 and 165 is 18480.
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 112 and 165?
First, calculate the GCD of 112 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 165 = 0 remainder 112 |
| 2 | 165 ÷ 112 = 1 remainder 53 |
| 3 | 112 ÷ 53 = 2 remainder 6 |
| 4 | 53 ÷ 6 = 8 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 88 | 6600 |
| 33 and 16 | 528 |
| 104 and 136 | 1768 |
| 109 and 41 | 4469 |
| 75 and 161 | 12075 |