Least Common Multiple (LCM) of 172 and 49
The least common multiple (LCM) of 172 and 49 is 8428.
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 49?
First, calculate the GCD of 172 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 49 = 3 remainder 25 |
| 2 | 49 ÷ 25 = 1 remainder 24 |
| 3 | 25 ÷ 24 = 1 remainder 1 |
| 4 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 48 | 144 |
| 151 and 128 | 19328 |
| 37 and 88 | 3256 |
| 75 and 128 | 9600 |
| 116 and 23 | 2668 |