Least Common Multiple (LCM) of 48 and 174
The least common multiple (LCM) of 48 and 174 is 1392.
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 174?
First, calculate the GCD of 48 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 174 = 0 remainder 48 |
| 2 | 174 ÷ 48 = 3 remainder 30 |
| 3 | 48 ÷ 30 = 1 remainder 18 |
| 4 | 30 ÷ 18 = 1 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 24 | 336 |
| 85 and 93 | 7905 |
| 154 and 110 | 770 |
| 83 and 78 | 6474 |
| 116 and 123 | 14268 |