Least Common Multiple (LCM) of 169 and 112
The least common multiple (LCM) of 169 and 112 is 18928.
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 169 and 112?
First, calculate the GCD of 169 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 112 = 1 remainder 57 |
| 2 | 112 ÷ 57 = 1 remainder 55 |
| 3 | 57 ÷ 55 = 1 remainder 2 |
| 4 | 55 ÷ 2 = 27 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 160 | 16160 |
| 103 and 57 | 5871 |
| 32 and 71 | 2272 |
| 160 and 183 | 29280 |
| 163 and 82 | 13366 |