Least Common Multiple (LCM) of 172 and 112
The least common multiple (LCM) of 172 and 112 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 172 and 112?
First, calculate the GCD of 172 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 112 = 1 remainder 60 |
| 2 | 112 ÷ 60 = 1 remainder 52 |
| 3 | 60 ÷ 52 = 1 remainder 8 |
| 4 | 52 ÷ 8 = 6 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 156 | 21372 |
| 142 and 103 | 14626 |
| 118 and 35 | 4130 |
| 122 and 175 | 21350 |
| 69 and 107 | 7383 |