Least Common Multiple (LCM) of 48 and 178
The least common multiple (LCM) of 48 and 178 is 4272.
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 178?
First, calculate the GCD of 48 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 178 = 0 remainder 48 |
| 2 | 178 ÷ 48 = 3 remainder 34 |
| 3 | 48 ÷ 34 = 1 remainder 14 |
| 4 | 34 ÷ 14 = 2 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 128 | 13440 |
| 57 and 179 | 10203 |
| 160 and 71 | 11360 |
| 144 and 183 | 8784 |
| 39 and 61 | 2379 |