Least Common Multiple (LCM) of 144 and 174
The least common multiple (LCM) of 144 and 174 is 4176.
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 144 and 174?
First, calculate the GCD of 144 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 174 = 0 remainder 144 |
| 2 | 174 ÷ 144 = 1 remainder 30 |
| 3 | 144 ÷ 30 = 4 remainder 24 |
| 4 | 30 ÷ 24 = 1 remainder 6 |
| 5 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 174 | 9222 |
| 46 and 112 | 2576 |
| 195 and 62 | 12090 |
| 26 and 12 | 156 |
| 105 and 32 | 3360 |