Least Common Multiple (LCM) of 112 and 172
The least common multiple (LCM) of 112 and 172 is 4816.
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 172?
First, calculate the GCD of 112 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 172 = 0 remainder 112 |
| 2 | 172 ÷ 112 = 1 remainder 60 |
| 3 | 112 ÷ 60 = 1 remainder 52 |
| 4 | 60 ÷ 52 = 1 remainder 8 |
| 5 | 52 ÷ 8 = 6 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 106 | 2968 |
| 105 and 177 | 6195 |
| 96 and 191 | 18336 |
| 170 and 59 | 10030 |
| 35 and 102 | 3570 |