Least Common Multiple (LCM) of 48 and 172
The least common multiple (LCM) of 48 and 172 is 2064.
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 48 and 172?
First, calculate the GCD of 48 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 172 = 0 remainder 48 |
| 2 | 172 ÷ 48 = 3 remainder 28 |
| 3 | 48 ÷ 28 = 1 remainder 20 |
| 4 | 28 ÷ 20 = 1 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 100 | 3400 |
| 174 and 33 | 1914 |
| 113 and 172 | 19436 |
| 80 and 119 | 9520 |
| 34 and 175 | 5950 |