Least Common Multiple (LCM) of 48 and 175
The least common multiple (LCM) of 48 and 175 is 8400.
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 175?
First, calculate the GCD of 48 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 175 = 0 remainder 48 |
| 2 | 175 ÷ 48 = 3 remainder 31 |
| 3 | 48 ÷ 31 = 1 remainder 17 |
| 4 | 31 ÷ 17 = 1 remainder 14 |
| 5 | 17 ÷ 14 = 1 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 96 | 1440 |
| 156 and 72 | 936 |
| 146 and 50 | 3650 |
| 159 and 23 | 3657 |
| 54 and 121 | 6534 |